- F THE /ERSH7 OF . J * ELEMENTS OP PHYSICS; OR, NATURAL PHILOSOPHY, GENERAL AND MEDICAL: WRITTEN FOE UNIVERSAL USE, IN PLAIN OR NON-TECHNICAL LANGUAGE; AND. CONTAINING NEf DISQUISITIONS AND PRACTICAL SUGGESTIONS. COMPRISED IN FIVE PARTS: 1. SOMATOLOGY, STATICS AND DYNAMICS. 2. MECHANICS. 3. PNEUMATICS, HYDRAULICS AND ACOUSTICS. 4. HEAT AND LIGHT. 5. ANIMAL AND MEDICAL PHYSICS. BY NEILL AKNOTT, M. D. , OF THE ROTALJ30LLEGE OF PHYSICIANS. L Xjpl A NEW EDITION, REVISED AND CORRECTED FROM THE LAST ENGLISH EDITION. WITH ADDITIONS. BY ISAAC HAYS, M. D. COMPLETE IN ONE VOLUME. i PHILADELPHIA: BLANCHARD AND LEA. 1856. Entered according to Act of Congress, in the year 1841, by LEA AND BLANCHARD, in 'the Clerk's Office of the District Court of the United States, in and for the Eastern District of Pennsylvania. GIFT Al ADVERTISEMENT AMERICAN PUBLISHERS THE very valuable and popular work of Dr. Arnott, has passed through several editions in this country, in the form in which it was originally published by the author, in separate parts. A new edition being now called for, the work has been carefully revised and corrected, and the whole condensed into one volume. In tkis form it cannot fail to be more acceptable to the public, and rendered more convenient and useful for the purposes of instruction in the various Colleges and Seminaries of Learning that have adopted it as a Class Book for their pupils. This volume embraces all that has been prepared or published by the author. VI INTRODUCTION. knowledge. Language thus, at the present moment of the world's existence, may be said to bind the whole human race of uncounted millions, into one gigantic rational being, whose memory reaches to the beginnings of written records, and retains imperishably the important events that have occurred ; whose judgment analyzing the treasures of memory, has discovered many of the sublime and unchanging laws of nature, and has buift on them all the arts of life, and through them piercing far into futurity, sees clearly many of the events that are to come, and whose eyes and ears, and obser- vant mind at this moment, in every corner of the earth, are watching and recording new phenomena, for the purpose of still better comprehending the magnificence and beautiful order of creation, and of more worthily adoring its beneficent author. It might be very interesting to show here, in minute detail, how the arts and civilization have progressed in accordance with the gradual increase of man's knowledge of the universe; but to do so would lead too far from the main subject. We deem it right, however, to make evident to the student the arousing truths, that the progress is not yet at an end; that it has been vastly more rapid in recent times than ever; and that it seems still to pro- ceed with increasing celerity : and we know not where the Creator has fixed the limits of the change ! Although there are thousands of years on the records of the world, our BACON, who first taught the true way to investi- gate nature, lived but the other day. NEWTON followed him, and illustrated his precepts by the most sublime discoveries which one man has ever made. HARVEY detected the circulation of the blood only two hundred years ago. ADAM SMITH, DR. BLACK and JAMES WATT were friends, and the last, whose steam-engines are now changing rapidly the condition of empires, may be said to be scarcely cold in his grave. JOHN HUNTER died not long ago ; HERSCHEI/S accounts of newly-discovered planets, and of the sublime struc- ture of the heavens, and DAVY'S account of chemical discoveries not less important to man, are in the late numbers of our scientific journals; illus- trious Britons these, and who have left worthy successors treading in their steps. On the continent of Europe during the same period, a corresponding constellation of genius has shone ; and LAPLACE was lately the bright star shining between the future and the past. But there is a change going on in the world, connected closely with the progress of science, yet distinct from it, and more important than a great part of the scientific discoveries; it is the diffusion of existing knowledge among the mass of mankind. Formerly, knowledge was shut up in convents and universities, and in books written in the dead languages or in books which, if in the living languages, were so abtruse and artificial, that only a few per- sons had access to their meaning ; and thus the human race being considered as one great intellectual creature, a smalljfraction only of its intellect was allowed to come into contact with science, and therefore into activity. The progress of science in those times was correspondingly slow, and the evils of general ignorance prevailed. Now, however, the strong barriers which con- fined the stores of wisdom have been thrown down, and a flood is overspread- ing the earth; old establishments are adapting themselves to the spirit of the age ; new establishments are arising ; the inferior schools are introducing improved systems of instruction ; and good books are rendering every man's fireside a school. From all these causes there is growing up an enlightened public opinion, which quickens and directs the progress of every art and science, and through the medium of a free press, although overlooked by many, is now rapidly becoming the governing influence in all the affairs of INTRODUCTION. VH man. In Great Britain, partly perhaps as a consequence of its insular situa- tion, which lessened among its inhabitants the dread of hostile invasion, and sooner formed them into a united and compact people, the progress of enlight- ened public opinion had been more decided than in any other state. The early consequences were more free political institutions ; and these gradually led to greater and greater improvements, until Britain became an object of admiration among the nation*. A colony of her children, imbued with her spirit, now occupies a magnificent territory in the new world of Columbus ; and although it has been independent as yet for only half a century, it already counts more people than Spain, and will soon be second to no nation on earth. The example of the Anglo-Americans has aided in rendering their western hemisphere the cradle of many other gigantic states, all free, and following, although at a distance, the like steps. In the still more recently discovered continent of Australasia, which is nearly as large as Europe, and is empty of men, colonization is spreading with a rapidity never before wit- nessed ; and that beautiful and rich portion of the earth will soon be covered with the descendants of free-bore and enlightened Englishmen. Thence, still onward, they or their institutions will naturally spread over the vast archipelago of the Pacific Ocean, a tract studded with islands of paradise. Such, then, is the extraordinary moment of revolution, or transit, in which the world at present exists ! And where, we may ask again, has the Creator predestined that the progress shall cease ? Thus far at least we know, that he has made our hearts rejoice to see the world filling with happy human beings, and to observe that the increase of the sciences can make the same spot maintain thousands in comfort and godlike elevation of mind, where with ignorance even hundreds had found but a scanty and degrading supply. The progress of knowledge which has thus led from former barbarism to present civilization, has gone on by certain remarkable steps, which it is easy to point out ; and which it is very useful to consider, because we thereby discover the nature of human knowledge, with the relations and importance of its different branches; and we obtain great facilities for studying. science, and for quickening its farther progress. The human mind, when originally directed to the almost infinity of objects in the universe around it, must soon have discovered that there were resem- blances among them ; in other words, that the infinity was only a repetition of a certain number of kinds. Among animals, for instance, it would distin- guish the sheep, the dog, the horse ; among vegetables, the oak, the beech, the pine ; among minerals, lime, flint, the metals, and so forth. And becom- ing aware that by studying an examplar of each kind, its limited power of memory might acquire a tolerably correct knowledge of the whole, while this knowledge would enable the possessors more easily to obtain what was useful to them, and to avoid what was hurtful, the desire for such knowledge must have arisen with the first exercise of reason. Accordingly, the pursuit of it has been unremitting, and the labour of ages has at last nearly com- pleted an arrangement of the constituent materials of the universe, under three great classes of MINERALS, VEGETABLES and ANIMALS; commonly called the three kingdoms of Nature, and .of which the minute* description is termed NATURAL HISTORY : and museums of natural history have been formed, which contain a specimen of almost every object included in these classes, so that now, a student within the limits of an ordinary garden, may be said to be able to examine the whole of the material universe. While men are examining the forms and other qualities of the bodies around them, they could not avoid noticing also the motions or changes going Vlll INTRODUCTION. on among bodies ; and here, too, they would soon make the grand discovery that there were resemblances in the multitude. Self-interest, as in the case of the bodies themselves, having prompted to careful classification, in the present day, as the result of countless observations and experiments made through the series of ages, we are enabled to say, that all the motions, or changes, or phenomena (words synonymous here) of the universe, are merely a repetition and mixture of a few simple manners, or kinds of motion or change, which are as constant and regular in every case as where they pro- duce the returns of day and night, and of the seasons. All these phe- nomena are referable to four distinct classes, which we call Physical, Chemi- cal, Vital and Mental. The simple expressions which describe them are denominated General Truths or Laws, of Nature, and as a body of know- ledge, they constitute what is called SCIENCE OF PHILOSOPHY, in contra- distinction of NATURAL HISTORY, already described. Now as man cannot, independently of a supernatural revelation, learn anything but what respects, 1st, the momentary state, past or present, of himself and the objects around him; and 2d, the manner in which the states are changed; Natural His- tory and Science, in the sense now explained, make up the whole sum of his knowledge of nature. To exemplify the process by which a general truth or law of nature is discovered, we shall take the physical law of gravity or attraction. 1st. It was observed that bodies, in general, if raised from the earth, and left un- supported, fell towards it; while flame, smoke, vapors, &c., if left free, ascended away from the earth. It was held, therefore, to be a very general law, that things had weight; but that there were exceptions in such mat- ters, as now mentioned, which were in their nature light or ascending. 2d. It was discovered that our globe of earth is surrounded by an ocean of air, having nearly fifty miles of altitude or depth, and of which a cubic foot taken near the surface of the earth, weighs about an ounce. It was then perceived that flame, smoke, vapor, &c., rise in the air only as oil rises in water, viz., because not so heavy as the fluid by which they are surrounded ; it followed, therefore, that nothing was known on earth naturally light, in the ancient sense of the 'word. 3d. It was found that bodies floating in water, near to each other, approached and feebly cohered ; that any contigu- ous hanging bodies were drawn towards each other, so as not to hang quite perpendicularly ; and that a plummet suspended near a hill was drawn to- wards the hill with force only so much less than that with which it was drawn towards the earth, viz , the weight of the plummet, as the hill was smaller than the earth. It was then proved that weight itself is only an instance of a more general mutual attraction, operating between all the con- stituent elements of this globe ; and which explains, moreover, the fact of the rotundity of the globe, all the parts being drawn towards a common cen- tre, as* also the form of dew-drops, rain-drops, globules of mercury, and of many other things ; which, still further, is the reason why the distinct particles of which any solid mass, as a stone or piece of metal, is composed, cling together as a mass, but which, when overcome by the repulsion of heat, allows the game particles to assume the form of a liquid or air. 4th. It was further observed, that all the heavenly bodies are round, and must, therefore, consist of material obeying the same law. 5th. And lastly, that these bodies, however distant, attract each other ; for that the tides of our ocean rise in obedience to the attraction of the moon, and become high or spring-tides, when the moon and sun operate in the same direction. Thus the sublime truth was at last made evident, and by the genius of the immor- INTRODUCTION. IX tal Newton, that there is a power of attraction connecting together the bodies of this solar system at least, and probably limited only by the bounds of the universe. Acquaintance with the laws of nature has been very slowly obtained, owing to that complexity of ordinary phenomena, which is produced by several laws operating together, and under great variety of circumstance. With respect to many laws of Chemistry and Life, men seem to be yet little far- ther advanced than they were with respect to the physical law of attraction, when they knew only that heavy things fell to the earth. But we have learned enough to perceive that the great universe is as simple and harmo- nious as it is immense ; and that the Creator, instead of interposing sepa- rately, or miraculously, in the common sense of the word, to produce every distinct phenomenon, has willed that all should proceed according to a few general laws. There is nothing in nature so truly miraculous and adorable as that the endless and beneficent variety of results which we see, should spring from such simple elements. In times of ignoranee, men naturally regarded every occurrence which they did not understand, that is to say, which they could not refer to a general law, as arising from a direct inter- ference of supreme power ; and thus, for many ages, among some nations still, eclipses and earthquakes, and many diseases, particularly those of the mind, and the winds and weather, were or are accounted miraculous. Hence arose, among heathens, many ceremonies, and sometimes even barbarous sacrifices, for propitiating or appeasing their offended deities ; but founded on expectations no more reasonable than if we should now pray to have the day of the year made shorter, or to have a coming eclipse averted. They had not yet risen to the sublime conception of the one God, who said, " Let there be light," and the light was; and who gave the whole of nature per- manent laws, which he allows men to discover for the direction of their con- duct in life laws so unchanging, that by them we can calculate eclipses backward or forward for thousands of years, almost without erring, by the time of one beat of a pendulum ; and as our knowledge of nature advances, we can anticipate and explain other events with equal precision. Even the wind and the rain, which, in common speech, are the types of uncertainty and change, obey laws as fixed as those of the sun and moon ; and already, as regards many parts of the earth, man can foretell them without fear of being deceived. He plans his voyages to suit the coming monsoons, and he prepares against the floods of the rainy seasons. The general laws of Nature, divisible, as stated above, into the four classes of, 1st, Physics, often called Natural Philosophy ; 2d, of Chemistry ; 3d, of Life, commonly called Physiology ; and 4th, of Mind, may be said to form the pyramid of Science, of which Physics is the base, while the others constitute succeeding layers in the order now mentioned ; the whole having certain mutual relations and dependencies well figured by the parts of a pyramid. We must describe them more particularly, to show these relations. Physics. The laws of Physics govern every phenomenon of nature in which there is any sensible change of place, being concerned alone in the greater part of these phenomena, and regulating the remainder which origi- nate from chemical action, and from the action of life. The great physical truths, as comprehended in the present day by man, are reduced to four, and are referred to by the words atom, attraction, repulsion and inertia. It gives an astonishing, but true idea of the nature and importance of methodi- cal Science, to be told that a man, who understands these words, viz., how the ATOMS of matter by mutual ATTRACTION approach and cling together X INTRODUCTION. to form masses, which are solid, liquid, or aeriform, according to the quan- tity or REPULSION of heat among them, and which, owing to their INERTIA or stubbornness, gain and lose motion, in exact proportion to the force of attraction or repulsion acting on then, understands the greater part of the phenomena of nature ; but such is the fact ! Solid bodies existing in con- formity with these truths, exhibit all the phenomena of Mechanics ; Liquids exhibit those of Hydrostatics and Hydraulics ; Airs, those of Pneumatics ; and so forth, as seen in the table of heads given below, at page xii. And the whole of this work is merely a list of the most interesting physical phenomena, arranged in classes under these heads. Chemistry. Had there been only one kind of substance or matter in the universe, the laws of Physics would have explained all the phenomena; but there are iron, and sulphur, and charcoal, and about fifty others, which to the present state of science, appear essentially distinct. Now these, when taken singly, obey the laws of Physics ; but when two or more of them are placed in contact, under certain circumstances, they exhibit a new order of phenomena. Iron and sulphur, for instance, brought together and heated, disappear as individuals, and unite into a yellow metallic mass, which, in most of its properties, is unlike to either : under other new circumstances, the two substances will again separate, and assume their original forms. Such changes are called chemical, (from an Arabic word signifying to burn, be- cause so many of them are effected by means of heat,) but during the changes, the substances are not withdrawn from the influence of the physi- cal laws, their weight or inertia, for instance, is not altered ; and indeed the phenomenon is merely a modification of general attraction and repul- sion. Many chemical changes, besides, are only the beginnings of purely mechanical changes, as when the new chemical arrangement produced by heat among the intimate atoms of gunpowder, causes the mechanical or physical motion of the sudden expansion or explosion. And all the mani- pulations of Chemistry, as the transferring of gases from vessel to vessel, the weighing of bodies, pounding, grinding, &c., are directed to Physics alone. Chemistry, then, is truly, as figured above, a superstructure on Physics, and cannot be understood or practised by a person who is ignorant of Physics. The chief departments of study involving the consideration of Chemical in conjunction with Physical laws, are enumerated in the table below, under the head of CHEMISTRY. Life. The most complicated state in which matter exists, is where, under the influence of life, it forms bodies with a curious internal structure of tubes and cavities, in which fluids are moving, and producing incessant internal change. These are called Organized Bodies, because of the various distinct parts or organs which they contain ; and they form two remarkable classes, the individuals of one of which are fixed to the soil, and are called Vegeta- bles ; and of the other, are endowed with power of locomotion, and are called Animals. The phenomena of growth, decay, death, sensation, self- motion, and many others, belong to life, but from occurring in material structures which subsist in obedience to the laws of Physics and Chemistry, the life is truly a superstructure on the other two, and cannot be studied independently of them. Indeed the greater part of the phenomena of organic life are merely chemical and physical phenomena, modified by an additional principle. The science of Life is divided into animal and vege* table Physiology (see the table below). Mind. The most important part of all science is the knowledge which man has obtained of the laws governing the operations of his own MIND. This department stands eminently distinct from the others, on several INTRODUCTION. XI accounts. Unlike that of organic life, which could not be understood until physics and chemistry had been, previously investigated, this had made extraordinary advances in a very early age, when the others, as methodical sciences, had scarcely begun to exist. In proof of this assertion we need only refer to the writings of the Greek' philosophers. The most brilliant discoveries and applications, however, were reserved for the moderns, as will occur to many readers, on perusing, in the table below, the several divisions of the subject, and recollecting the honoured names which are now associa- ted with each. It is truly admirable to see the modern analysis, deducing from a few simple laws of mind, act the subordinate departments, just as it deduces mechanics, hydrostatics, pneumatics, &c., from the laws of physics : and let us hope that sound opinions on this subject, ensuring human happi- ness, and therefore, beyond comparison, more important than any other knowledge, will soon be widely spread. The crowning science of Mind, although in certain respects independent of the science of Matter, is still closely allied to them in the following ways. The faculties of the mind are originally awakened or called into activity solely by the impressions of mat- ter or external nature ; all the language used in speaking of mind and its operations, is borrowed from matter ; and many mental emotions are entirely dependent on bodily conditions. The science of Mind, therefore, cannot be studied until after knowledge acquired of an external nature; and cannot be studied extensively until that knowledge be extensive. Quantity. To express most of the facts an J laws of Physics, Chemistry and Life, terms of QUANTITY are required, as when we speak ( f the magni- tude of a body, or say, that the force of attraction between two bodies diminishes, in a certain proportion, as their distance increases. Hence arises the necessity of having a set of fixed measures or standards, with which to compare all other quantities. Such measures have been adopted; and they are, for NUMBERS, the fingers, Jives and tens; for LENGTH, the human foot, cubit, pace, &c. ; and lately the second' s pendulum and the French metre, (taken from the magnitude of our globe); for SURFACES, the simplest forms of circle, square, triangle, &c., compared among themselves by the lengths of their diameters or other suitable lines; and for SOLID BULK, the corres- ponding simple solids, of globe., cube, pyramid, cone, &c. t similarly compared by the lengths of diameters or of other lines of dimension. The rules for applying these standards to ail possible cases, and for comparing all kinds of quantities with each other, constitute a body of science, called the Science of Quantity, the Mathematics. It may be considered as a subsidiary depart- ment of human science, created by the mind itself, to facilitate the study of the others. Supposing description of particulars, or Natural History, to be studied along with the different parts of the System of Science sketched in the table, there will be included in the scheme the whole knowledge of the universe which man can acquire by the exercise of his own powers : that is to say, what he can acquire independently of a supernatural Revelation. And on this knowledge all his arts are founded, some of them on the single part of Physics, as that of the machinist, architect, mariner, carpenter, &c. ; some on Chemistry, (which includes Physics,) as that of the miner, glass- maker, dyer, brewer, &c. ; and some on Physiology, (which includes much of Physics and Chemistry,) as that of the scientific gardener or botanist, agri- culturist, zoologist, &c. The business of teachers of all kinds, and of governors, advocates, linguists, &c., &c., respects chiefly the science of Mind. The art of medicine requires in its professor a comprehensive knowledge of all the departments. xu INTRODUCTION. TABLE OF SCIENCE AND ART. 1. PHYSICS. 2. CHEMISTRY. Mechanics, Hydrostatics, Hydraulics, Pneumatics, Acoustics, Heat, Optics, Electricity, Astronomy, &c. Simple substances, Mineralogy, Geology, Pharmacy, Brewing, Dyeing, Tanning, &c. 3. LIFE. Vegetable Physiology. Botany, Horticulture, Agriculture, &c. Animal Physiology, Zoology, Anatomy, Pathology, Medicine &c. 4. MIND. Intellect, Logic, Mathematics, &c. Motives to action, Emotions and Passions, Morals, Government, Political Economy, Theology, Education. In the first stages of education, viz., during the years of childhood and youth, the learning acquired is necessarily of the most mixed kind, and much of it is determined by what is called accident; but from the mutual dependence of the different departments of science, as explained in the pre- ceding paragraphs, it follows that with a view to complete erudition', the order exhibited in "The Table/' is that in which they should afterwards be studied, so as to prevent repetitions and anticipations, and to diminish, as much as possible, the labor of acquirement. Every man may be said to begin his education, or acquisition of know- ledge, on the day of his birth. Certain objects, repeatedly presented to the infant, are, after a time, recognized and distinguished. The number of objects thus known gradually increases, and from the constitution of the mind, they are soon associated in the recollection, according to their resem- blances, or obvious relations. Thus, sweetmeats, toys, articles of dress, &c., soon form distinct classes in the memory and conceptions. At a later age, but still very early, the child distinguishes readily between a mineral mass, a vegetable, and an animal; and thus his mind has already noted the three great classes of natural bodies, and has acquired a certain degree of acquaint- ance with Natural History. He also soon understands the phrases a a falling body," "the force of a moving body," and has therefore a perception of the INTRODUCTION. Xlll great physical laws of gravity and inertia. Then having seen sugar dissolved in water, and wax melted round the wick of a burning candle he has learned some phenomena of Chemistry. And having obs'erved the conduct of the domestic animals, and of the persons about him, he has begun his acquaint- ance with Physiology, and the science of mind. Lastly, when he has learned to count his fingers and his sugar plums, and to judge of the fairness of the division of a cake between himself and brothers, he has advanced into Arith- metic and Geometry. Thus within a year or two, a child of common sense has made a degree of progress in all the great departments of human science ;' and in addition has learned to name objects, and to express feelings, by the arbitrary sounds of language. Such, then, are the beginnings or founda- tions of knowledge, on* which 'future years of experience, or methodical education, must rear the superstructure of the more considerable attain- ments which befit the various conditions of men in a civilized com- munity. In the course of the preceding disquisition, we have seen that Physics, or Natural Philosophy, the subject of the present volume, is fundamental to the other parts, and is therefore that of which a knowledge is indispensable. Bacon truly calls it " the root of the sciences and arts." That its import- ance has not been marked by the place which it has held in common systems of education, is owing chiefly, 1st, to the misconception that a knowledge of technical mathematics was a necessary preliminary ; and, 2d, to an opinion, also erroneous, that the degree of acquaintance with Physics which all persons acquire by common experience, is sufficient for common pur- poses ; now it is true, that the toys of childhood, as the windmill, ball, syphon, tube, and a hundred others, furnish so many exemplifications of the laws of Physics, and may well be called a philosophical apparatus ; but they give information which is exceedingly vague, and not at all such as is absolutely requisite in the practice of many of the arts. If, then, the study of Physics be so easy as now appears, and so important as we shall try still farther to show, there can be no excuse for neglecting it. =- The greatest sum of knowledge acquired with the least trouble is, perhaps, that which comes with the study of the few simple truths of Physics. To the man who understands these, very many phenomena, which, to the unin- formed, appear prodigies, are only beautiful illustrations of his fundamental knowledge, and this he carries about with him, not as an oppressive weight, but as a charm supporting the weight of other knowledge, and enabling him to add to his valuable store every new fact of importance which may offer itself. With such a principle of arrangement, his information, instead of resembling loose stones or rubbish thrown together in confusion, becomes as a noble edifice, of correct proportions and firm contexture, and is acquiring greater strength and consistency with the experience of every day. It has been a common prejudice, that persons thus instructed in general laws, had their attention too much divided, and could know nothing perfectly. But the very reverse is true; for general knowledge renders all particular knowledge more clear and precise. The ignorant man may be said to have charged his hundred books of knowledge, to use a rude simile, with single objects, while the informed man makes each support a long chain, to which thousands of kindred and useful things are attached. The laws of Philosophy may be compared to keys which give admission to the most delightful gar- dens that fancy can picture ; or to a magic power, which unveils the face of the universe, and discloses endless charms of which ignorance never dreams. The informed man, in the world, may be said to be always sur- xiv INTRODUCTION. rounded by what is known and friendly to him, while the ignorant man is as one in a land of strangers and enemies. A man reading a thousand volumes of ordinary botfks as agreeable pastime, will receive only vague impressions; but he who studies the methodized Book of Nature, converts the great universe into a simple and sublime history, which tells of God, and may worthily occupy his attention to the end of his days. We have said already, that theJaws of Physics govern the great natural phenomena of Astronomy, the tides, winds, currents, &c. We will now mention some of the artificial purposes to which man's ingenuity has made the same laws subservient. Nearly all that the civil engineer accomplishes, ranges under the head of Physics. Let us take, for instance, the admirable specimens scattered over the British Isles : the numerous canals for inland traffic ; the dock to receive the riches of the world, pouring towards us frbm every quarter; the many harbours offering safe retreat to the storm-driven mariner ; the mag- nificent bridges which every where facilitate intercourse ; hills bored through to open ways for commerce by canals, common roads and rail-roads, the canals in some places being supported, like the roads, on arches across valleys or above rivers, so that here and there the singular phenomenon is seen of one vessel sailing directly over another ; vast tracts of swamps or fen-land drained and now serving for agriculture ; the noble light-house, rearing its head amidst the storm, while the dweller within trims his lamp in safety, and guides his endangered fellow-creature through the perils of the night, &c., &c. In Holland, great part of the country has been won and is now preserved from the sea, by the same almost creating power, and now rich cities and an extended garden smile, where, as related by Caesar, were formerly only bogs and a dreary waste. As a general picture, it is interesting to consider, that in many situations on earth where formerly the rude savage beheld the cataract falling among the rocks, and the wind bending the trees of the forest, and sweeping the clouds along the mountain's brow, or whitening the face of the ocean, and regarding these phenomena with awe and terror, as marking the agency of some great but hidden power, which might destroy him; in the same situa- tions now, his informed son, who works with the laws of nature, can lead the waters of the cataract, by sloping channels, to convenient spots, where they are made to turn his mill-wheel, and to do his multifarious work ; the rushing winds, also, he makes his servant, by rearing in their course the broad-vaned wind-mill, which then performs a thousand offices for its master, man; and the breezes which whiten the ocean are caught in his expanded sails, and are made to waft their lord and his treasures across the deep, for his pleasure or his profit. In Architecture, also, Physics in supreme, and has directed the construc- tion of the temples, pyramids, domes and palaces which adorn the earth. In respect to machinery, generally, Physics is the guiding light. There are, for instance, the mighty steam-engine; machines for spinning and. weaving, and for moulding other bodies into various shapes, yea, even iron itself, as if it were plastic clay; wind-mills and water-mills, and wheel carriages; the plough and implements of husbandry ; artillery and the fur- niture of war; the balloon, in which man rides triumphantly above the clouds, and the diving-bell, in which he penetrates the secret caverns of the deep ; the implements of the intellectual arts, of printing, drawing, painting, sculpture, &c. ; musical instruments, optical and mathematical instruments, and a thousand others. INTRODUCTION. XV But Physics is also an important foundation of the healing art. The medi- cal man, indeed, is the engineer pre-eminently ; for it is in the animal body that true perfection and the greatest variety of mechanism are found. Where, to illustrate Mechanics, is to be found a system of levers and hinges, and moving parts, like the limbs of an animal body ; where such an hydraulic apparatus, as in the heart and blood-vessels ; such a pneumatic apparatus, as in the breathing chest ; such acoustic instruments, as in the ear and larynx ; such an optical instrument, as in the eye ; in a word, such variety and perfection, as in the whole of the visible anatomy ? All these struc- tures, then, the medical man should understand, as the watchmaker knows the parts of a time-piece about which he is employed. The watchmaker, unless he can discover where a pin is loose, or a wheel injured, or a particle of dust adhering, or oil wanting, &c., would ill succeed in repairing an injury; and so, also, of the ignorant medical man in respect to the human body. Yet will it be believed, that there are many medical men who neither understand mechanics, nor hydraulics, nor pneumatics, nor optics, nor acoustics, beyond the merest routine ; and that systems of medical education are set forth at this day which do not even mention the depart- ment of Physics ! That such is the case, furnishes an illustration of what is stated in the beginning of this essay, viz., that the sciences and arts are progressive, and that perfect methods of education must arise gradually, like all other things of human contrivance. It is within the recollection of persons now living, that political economy was discovered to be a grand foundation of the art of government, indicating means of security against many national misfortunes common in former times, yea, even against famine and war. And the day is not distant, when the members of the medical pro^ssion generally will understand how much the correct knowledge of animal structure and function, and of many remedies, must depend on pre- cise acquaintance with Physics. Besides the more strictly professional matters contained in the medical sections of the present work, there are many others scattered through it which greatly interest the medical man ; such are the subjects of meteorology, climate, ventilation and warming of dwellings, specific gravities, &c., &c. The laws of Physics having an influence so extensive as appears from these paragraphs, it need not excite surprise that all classes of society are at last discovering the deep interest they have to understand them. The lawyer finds that in many of the causes tried in his courts, an appeal must be made to Physics, as in cases of disputed inventions; accidents in navigation, or among carriages, steam-engines, and machines generally ; questions arising out of the agency of winds, rains, water-currents, &c. : the statesman is con- stantly listening to discussions respecting bridges, roads, canals, docks, and the mechanical industry of the nation : the clergyman finds ranged among the beauties of nature, the most intelligible and striking proof of God's wis- dom and goodness; the sailor in his ship has to deal with one of the most admirable machines in existence : soldiers, in using their projectiles, in marching where rivers are to be crossed, woods to be cut down, roads to be made, towns to be besieged, &c., are dependent chiefly on their knowledge of Physics : the land-owner, in making improvements on his estates, building, draining, irrigating, road-making, &c. : the farmer equally in these particu- lars, and in all the machinery of agriculture; the manufacturer, of course; the merchant who selects and distributes over the world the products of manufacturing industry all these are interested in Physics ; then also the man of letters, that he may not, in drawing his illustrations from the material XVI INTRODUCTION. world, repeat the scientific heresies and absurdities which have heretofore prevailed, and which, by shocking the now better-informed public, exceed- ingly lower the estimation in which such specimens of the Belles Lettres are held, and lessen their general utility; and lastly, parents of either sex, whose conversation and example have such powerful effect on the character of their children, who when grown up, are to fill all the stations in society; all should study Physics, as one important part of their education. And it is for such reasons that Natural Philosophy is becoming daily more and more a part of common education. In our cities now, and even in an ordinary dwelling-house, men are surrounded by prodigies of mechanic art, and cannot submit to use these, regardless of how they are produced, as a horse is regardless of how the corn falls into his manger. A general diffu- sion of knowledge, owing greatly to the increased commercial intercourse of nations, and therefore to the improvements in the physical departments of astronomy, navigation, &c., is changing every where the condition of man, and elevating the human character in all ranks of society. In remote times the inhabitants of the earth were generally divided into small states or socie- ties, which had few relations of amity among themselves, and whose thoughts and interests were confined very much within their own little territories and rude habits. In succeeding ages, men found themselves belonging to larger communities, as where the English heptarchy was united ; but still distant kingdoms and quarters of the world were of no interest to them, and were often totally unknown. Now, however, every one feels that he is a member of one vast civilized society, which covers the face of the earth ; and no part of the earth is indifferent to him. In England, for instance, a man of small fortune may cast his looks around him, and say with truth and exultation, " I am lodged in a house which affords me conveniences and comforts w^ich some centuries ago, even a king could not command. Ships are crossing the seas in every direction, to bring me what is useful to me from all parts of the earth. In China, men are gathering the tea-leaf for me ; in America, they are planting cotton for me ; in the West Indies, they are preparing my sugar and my coffee; in Italy, they are feeding silk-worms for me; in Saxony, they are shearing the sheep to make me clothing; at home, power- ful steam-engines are spinning and weaving for me, and making cutlery for me, and pumping the mines that minerals useful to me may be procured. Although my patrimony was small, I have post-coaches running day and night on all the roads to carry my correspondence ; I have roads and canals, and bridges, to bear the coal for my winter fire ; nay, I have protecting fleets and armies around my happy country, to secure my enjoyments and repose. Then I have editors and printers, who daily send me an account of what is going on throughout the world, among all these people who serve me. And in a corner of my house I have BOOKS ! the miracle of all my possessions, more wonderful than the wishing-cap of the Arabian Tales : for they trans- port me instantly, not only to all places, but to all times. By my books I can conjure up before me, into vivid existence, all the great and good men of antiquity ; and for my individual satisfaction I can make them act over again the most renowned of their exploits, the orators declaim for me ; the historians recite ; the poets sing ; and from the equator to the pole, or from the beginning of time until now, by my books, I can be where I please." This picture is not overcharged, and might be much extended, such being God's goodness and providence, that each individual of the civilized millions dwelling on the earth, may have nearly the same enjoyment as if he were the single lord of all. INTRODUCTION. Xvij Reverting to the importance of Natural Philosophy as a general study, it may be remarked that there is no occupation which so much strengthens and quickens the judgment. This pra ; se has usually been bestowed on the Ma- thematics, although a knowledge of abstract Mathematics existed with all the absurdities of the dark ages ; but a familiarity with Natural Philosophy which comprehends Mathematics, and gives tangible and pleasing illustra- tions of the abstract truths, seems incompatible with the admission of any gross absurdity. A man whose mental faculties have been sharpened by acquaintance with these exact sciences in their combination, and who has been engaged, therefore, in contemplating real relations, is more likely to discover truth in other questions, and can better defend himself against sophistry of every kind. We cannot have clearer evidence of this than in the history of the sciences, since the Baconian method of reasoning by indi- cation took place of the visionary hypotheses of preceding times. Until then, even powerful minds did not recoil from the most absurd theories on all sub- jects. Astronomy was mixed with Astrology ; Chemistry with Alchemy ; Physiology with the singular hypotheses which preceded the discovery of the circulation of the blood ; Politics with the errors of monopolies, prohibitions, balance of trade, &c. Even Religion itself, in various ages and countries, has felt the influence of the state of the public mind as to solid attainments. To a man with the knowledge of nature which we now possess, the fables .and licentious abominations of the Greek and Roman theologies are shocking indeed ; as are the religions of the God of Fire in China, of Vishnoo in India, of Mahomet's imposture and pretended miracles, &c. But the enlight- ened Christian minister earnestly recommends the study of nature ; first because from contemplating the beauty of creation, with the wisdom and benevolent design manifest in all its parts, there spring up in every unde- praved mind those feelings of admiration and gratitude, which constitute the adoration of natural religion, and which form, as shown by many estimable writers on Natural Theology, a fit foundation for the sublime doctrine of immortality, and secondly, because a Revelation being probable only by the miracles occurring at its establishment; to enable men to distinguish between miracles and the usual course of nature, a perfect knowledge of that course, or of Natural Philosophy, is essential : all the false religions of antiquity were founded on, and upheld by pretended miracles. As regards the ques- tion of immortality, even independently of Revelation, no man who con- templates the order and beauty of the material world, and then thinks on the hideous deformities of the moral world where vice so often triumphs, and modest virtue pines and dies can for a moment believe that they are the work of the same author, unless there be a hereafter of retribution ; and feeling thus that eternal justice requires another state for man, he embraces with delight the cheering promises of immortality. There have been, how- ever, at various times, even among Christians, sincere, but weak-minded or ill-informed men, who decried the study of the natural sciences, as inimical to true religion ; as if God's ever-visible and magnificent revelation of his attributes in the structure of the universe could be at variance with any other revelation. But such prejudices are now quickly passing away. Wherever considerable knowledge of nature exists, debasing and gloomy superstition must cease. It is not the abject terror of a slave which is in- spired by contemplating the majesty and power of our God, displayed in his works, but a sentiment akin to the tender regard which leads a favored child to approach with confidence a wise and indulgent parent. It remains for the author now only to say a few words with respect to the 2 XV111 INTRODUCTION. present work. He was originally led to the undertaking with the view of supplying the desideratum in medical literature, of a treatise on Medical Physics; but soon perceiving that the preliminary investigation of General Physics, necessary to adapt the work to medical readers, would require to be nearly as extensive as it would for general readers, and reflecting that every person of liberal education must now possess such a book, not to be read once and then thrown aside as a novel is, but to be frequently consulted as a manual, he determined to make his book as complete and as extensively useful as possible. He has been encouraged during his labor, by the belief that the growing light of science, which now exhibits more clearly the na- tural relations of the different departments of study, as attempted to be por- trayed in the preceding pages, might enable him to avoid some of the defects of former elementary treatises, and to add features of novelty and improve- ment to his own. The sections on Animal Physics were, of course, written for medical men ; and a great service will be rendered by the work, if it only awakens them to a just sense of the importance of Physics as one of the foundations of their art. But even for general readers there are few parts of these sections which the author would exclude. There is nothing more admirable in nature than the structure and functions of the human body, and there are many reasons why no liberal mind should be careless of the study. The details here given are not more anatomical than the illus- trations from the animal economy contained in the common treatises on Natural Theology. From the attempt in this work to compress into the smallest possible ppace the greatest possible sum of scientific information, few historical details have been admitted, whether relating to the distin- guished men who have benefitted the world as authors or inventors, or to the history of the progress of science : such details form an interesting, but distinct branch of study. The author must not conclude without observing, that no treatise on Na- tural Philosophy can save, to a person desiring full information on the sub- ject, the necessity of attendance on experimental lectures or demonstrations. Things that are seen, and felt, and heard, that is, which operate on the ex- ternal senses, leave on the memory much stronger and more correct impres- sions than where the conceptions are produced merely by verbal description, however vivid. And no man has ever been remarkable for his knowledge of Physics, Chemistry, or Physiology, who has not had practical familiarity with the objects. With reference to this familiarity, persons who take a philanthropic interest in the affairs of the world, must observe, with much pleasure the now daily increasing facilities of acquiring useful knowledge, afforded by the scientific institutions formed and forming, not only through this kingdom, but through most civilized nations. Bedford Square, 1st March, 1827. ELEMENTS NATURAL PHILOSOPHY. SYNOPSIS, OR GENERAL REVIEW. IF it excite our admiration that a varied edifice, or even a magnificent city can be constructed of stone from one quarry, what must our feeling be to learn how few and simple the elements are out of which the sublime fab- ric of the universe, with all its orders of phenomena, has arisen, and is now sustained, These elements are general . facts and laws which human sagacity is able to detect, and then to apply to endless purposes of human advantage. Now the four words, atom, attraction, repulsion, inertia, point to four general truths, which explain the greater part of the phenomena of nature. Being so general, they are called physical truths, from the Greek word signifying nature as also " truths of Natural Philosophy," with the same meaning, and sometimes " mechanical truths/' from their close relation to ordinary machinery. These appellations distinguish them from the remain- ing general truths, namely the chemical truths, which regard particular substances, and the vital and mental truths, which have relation only to living beings. And even in the cases where a chemical or vital influence operates, it modifies, but does not destroy, the physical influence. By fixing the attention, then, on these four fundamental truths., the student obtains, as it were, so many keys to unlock, and lights to illuminate the secrets and treasures of nature. 1st. ATOM. Every material mass in nature is divisible into very minute indestructible and unchangeable particles, as when a piece of any metal is bruised, broken, cut, dissolved, or otherwise transformed, a thousand times, but can always be exhibited again as perfect as at first. This truth is conveniently recalled by giving to the particles the name atom, which is a Greek term, signifying that which cannot be further cut or divided, or an exceeding minute resisting particle. 2d. ATTRACTION. It is found that the atoms above referred to, whether separate or already joined into masses, tend towards all other atoms or masses, as when the atoms of which any mass is composed are, by an in- visible influence, held together with a certain degree of force ; or when a block of stone is similarly held down to the earth on which it lies; or when the tides on the earth rise towards the moon. These facts are conveniently 20 SYNOPSIS. / recalled by connecting with them the word Attraction (a drawing together) or gravitation. 3d. REPULSION. Atoms under certain circumstances, as of heat diffused among them, have their mutual attraction countervailed or resisted, and they tend to separate ; as when ice heated melts into water, or when water heated bursts into steam, or when gunpowder ignited explodes. Such facts are conveniently recalled by the term Repulsion (a thrusting asunder.) 4th. INERTIA. As a fly-wheel made to revolve, at first offers resistance to the force moving it, but gradually acquires speed proportioned to that force, and then resists, being again stopped, in proportion to its speed, so all bodies or atoms in the universe have about them, in regard to motion, what may be figuratively called a stubb.orness, tending to keep them, in their existing state, whatever it may be in other words, they neither acquire motion, nor lose motion, nor bend their course in motion, but in exact proportion to some force applied. Many of the motions now going on in the universe with such regularity as that turning of the earth which produces the phe- nomena of day and night are motions which began thousands of years ago, and continue unvarying in this way. Such facts are conveniently recalled by the term inertia applied to them. A person comprehending fully the import of these four words, that is to say, having present to his mind numerous good types or exemplars of the facts referred to them, may predict or anticipate correctly, and may control very many of the facts and phenomena which the extended experience of a life can display to him ; and such a person is commonly said to know the causes or reasons of things and events. Now it is important here to observe, that when a person gives a reason or explanation of any fact, other than that it is a fact, or than that the Creator has willed it, he is merely, although he may not be aware of this, showing its resemblance to many other facts, no one of which he understands better than itself and what he calls a general truth, or law, or principle, is merely an expression for the observed but unaccountable resemblance of the facts. Thus, when a man says that a stone falls because of attraction or gravitation, he only uses a word which recalls thousands of instances which he has witnessed of one body approach- ing another; but by any cause of the approach, other than that God has willed it, is to him utterly unknown. Should men, in the course of their researches, discover that the phenomena now classed by them under the heads of attraction and repulsion, although apparently opposite, are really as closely allied as they already know the rising of a balloon and the falling of a stone to be (the balloon rises like a cork in water, being pushed up by the fluid air around it, heavier than it, and seeking to descend,) they will not have discovered a new cause, but a new resemblance, (new to them) among phenomena, and will only have advanced one step farther in perceiving the simplicity of creation. In accordance with these views, it will be found that this volume is chiefly an extensive display of the ^rnost important phenomena of nature and art, classified so as to be explained by the f our physical truths, and mutually to illustrate one another. They will be listributed under the following heads or divisions : SYNOPSIS. 21 * PAKT I. CONSTITUTION OP MASSES, MOTIONS AND FORCES. The four fundamental truths extensively examined, and used to explain generally, in Section 1. The nature or constitution of the material masses which compose the universe ; (a department technically called SOMATOLOGY, from Greek words signifying a discourse on body.} 2. The motions or phenomena going on among the masses; a department including the common divisions of STATICS (things stationary or at rest,) and DYNAMICS (what relates to force or power.} PART II. PHENOMENA OP SOLIDS. The four truths explaining the peculiarities of state and motion among solid bodies : a department called, in a restricted sense, MECHANICS, (from the Greek, and signifying machine.) PART III. PHENOMENA OP FLUIDS. The truths explaining the peculiarities of state and motion among fluid bodies : a department called HYDRODYNAMICS (from Greek words signify- ing water &M& force) Section 1. HYDROSTATICS (water at rest or in equilibrium.) 2. PNEUMATICS (air phenomena.) 3. HYDRAULICS (water or fluid in motion.) 4. ACOUSTICS (phenomena of sound and hearing.) PART IY. PHENOMENA OP IMPONDERABLE SUBSTANCES. The truths aiding to explain the more recondite phenomena of IMPON- DERABLE SUBSTANCES, under the heads of Section 1 . HEAT or Caloric. 2. LIGHT or Optics. PART Y. ANIMAL AND MEDICAL PHYSICS. In this part will be ranged the most interesting illustrations afforded by the animal economy, constituting ANIMAL AND MEDICAL PHYSICS. As no man can well understand a subject of which he does not carry a distinct outline in his mind, it is recommended to the reader of this work to study the general synopsis, and the analysis placed at the heads of the chapters and sections, until the memory be well impressed with them. 22 . CONSTITUTION OF MASSES PART I. THE FOUR FUNDAMENTAL TRUTHS MINUTELY EXAMINED, AND USED TO EXPLAIN GENERALLY, FIRST, THE NATURE OR CONSTITUTION OF THE MATERIAL MASSES WHICH COMPOSE THE UNIVERSE, AND SECONDLY, THE MOTIONS OR PHENOMENA GOING ON AMONG THEM. SECTION L THE CONSTITUTION OF MASSES. ANALYSIS OF THE SECTION. The visible universe is built up of very minute indistructible ATOMS called matter, which by mutual ATTRACTION, cohere or cling together in masses of various form and magnitude. The atoms are more or less approxi- mated, according to the quantity or REPULSION of heat among them, and hence arise the three remarkable forms in the masses, of solid, liquid and air, which mutually change into each other with change in the quantity of heat. Certain modifications of attraction and repulsion produce the subordinate peculiarities of state called crystal, dense, hard, elastic, brittle, malleable, ductile and tenacious. " Minute Indestructible ATOMS."* THAT the smallest portion of any substance which the human eye can per- ceive, is still a mass of many ultimate atoms or particles, which may be separated from each other, or newly arranged, but which cannot individu- ally be hurt or destroyed, is deduced from such facts as the following : A particle of powdered marble, hardly visible to the naked eye, still ap- pears to the microscope a block susceptible of indefinite division ; and, when it is broken by fit instruments, until the microscope can hardly discover the separate particles of fine powder, these may be yet further divided, by solution in an acid; the whole becoming then absolutely invisible, as part of a transparent liquid. A small mass of gold may be hammered into thin leaf, or drawn into fine wire, or cut into almost invisible parts, or liquefied in a crucible, or disolved in an acid, or dissipated by intense heat into vapour ; yet, after any and all these changes, the atoms can be collected again to form the original mass of gold, without the slightest diminution or change. And all the substance of * The different heads or titles, which appear thus, throughout the work, between in- verted commas, are the successive portions of the Analysis, detached for separate consideration. The reader is particularly requested to re-peruse the analysis at the several interruptions, that he may have constantly before him that clear view of the general relations among the different parts of the subject, which is essentially to a per- fect understanding of it. CONSTITUTION OF MASSES. 23 elements of which our globe is composed, may thus be cut, torn, bruised, ground, &c., a thousand and a thousand times, but are always recoverable as perfect as at first. And with respect to delicate combinations of these elements, such as exist in animal and vegetable bodies, although it be beyond human art, originally to produce, or even closely to imitate many of them for we cannot build up a feather or a rose still, in their decomposition and apparent destruction, the accomplished chemist of the present day does not lose a single atom. The coal which burns in his apparatus, until only a little ash remains behind, or the wax -taper that seems to vanish altogether in flame, or the portion of animal flesh which putrefies, and gradually dries up and disappears present to us phenomena which are now proved to be only changes of connection and arrangement among the indestructible ultimate atoms ; and the chemist can offer all the elements again, mixed or separate as desired, for any of the useful purposes to which they are severally applicable. When the funeral piles of the ancients, with their charge of human remains, appeared to be wholly consumed, and left the idea with survivors that no base use could be made, in after time, of what had been the material dwelling of a noble or beloved spirit, the flames had only, as it were, scattered the enduring blocks of which a former edifice had been constructed, but which were soon to serve again in new combinations. Facts to be stated under the heads of " chemical composition" and " crys- tal," will prove, that the ultimate particles of any substance must be, among themselves, perfectly similar. " Minute." (Read the Analysis, page 22.) The following are interesting particulars in the arts or in nature, helping the mind to conceive how minute the ultimate atoms of matter must be. Goldbeaters, by hammering, reduce gold to leaves so thin, that 360,000 must be laid upon one another to produce the thickness of an inch. They are so thin, that if formed into a book, 1,800 would occupy only the space of a single leaf of common paper ; and an octavo volume an inch thick would have as many pages as the books of a well-stocked ordinary library contain- ing 1,800 volumes of 400 pages each ; yet those leaves are perfect, or free from holes, so that one of them laid upon any surface, as in gilding, gives the appearance of solid gold. Still thinner than this is the coating of gold, uponithe silver wire of what is called gold lace ; and we know not that such coating is of only one atom thick. If we place a piece of this wire in nitric acid, so as to dissolve the silver within, the gold coating remains as a metallic tube of exquisite tenuity. Platinum can be drawn into wire much finer than human hair. A grain of blue vitriol or carmine, will tinge a gallon of water, so that in every drop the colour may be perceived. A grain of musk will scent a room for twenty years, and will have lost but little of its weight. The carrion crow seems to smell its food at a distance of many miles. The thread of the silk worm is so small, that many folds have to be twisted together to form our finest sewing thread; but that of the spider is smaller still, for two drachms of it by weight would reach from London to - Edinburgh, or 400 miles. In the milk of a cod-fish, or in water in which certain vegetables have 24 CONSTITUTION OF MASSES. been infused, the microscope discovers animalcules, of which many thou- sands together do not equal in bulk a grain of sand ; yet these have their blood and other subordinate parts like larger animals ; and, indeed, nature, with a singular prodigality, has supplied many of them with organs as com- plex as those of the whale or elephant. Now the body of an animalcule consists of the same elementary substances, or ultimate atoms, as the body of man himself. In a single pound of matter, it thus appears, that there may be more living creatures than of human beings on the face of this globe, What scenes has the microscope laid open to the admiration of the philoso- phic inquirer. Water, mercury, sulphur, or, in general, any substance, when sufficiently heated, rises as invisible vapour or gas ; in other words, is made to assume the aeriform state. Great heat, therefore, would cause the whole of the material universe to disappear, the previously most solid bodies' becoming as invisible and impalpable as the air we breathe. Utter annihilation would seem but one stage beyond this. "MaMtrS* The inconceivable minuteness of ultimate atoms, as shown above, has led some inquirers to doubt whether there really be matter ; that is to say, whether what we call substance or matter have existence or not. In answer to this it has been usual to adduce, besides the weights of the substances, and the proofs of indestructibility already mentioned, which seems conclu- sive, the fact that every kind or portion of matter obstinately occupies some space to the exclusion of all other matter from that particular space. This occupancy of space is the simplest and most complete idea which we have of material existence. The awkward word impenetrability has been used to express it, with reference of course to the individual atoms. The following are elucidations : We cannot push one billiard-ball into the substance of another, and then a second, and then a third, and so on ; or the material of the universe might be absorbed in a point. A mass of iron on a support will resist the weight of thousands of pounds laid upon it and pressing to descend into its place ; and although a very great weight might crush or break it into pieces, still one particle would not be annihilated. In a forcing pump, or in Braham's water-press, millions of pounds can not push the piston down, unless the water below it be allowed to escape. A weight laid upon bladders full of air, or on the piston handle of a closed air-pump, is supported in the same manner. A quantity of air escaping from a vessel under water ascends through the water as a bubble displacing its bulk of water in its way. A glass tube, left open at bottom, while the thumb closes the top, if pressed from air into water, is not filled with water, because the air contained in it resists ; but if the air be allowed to escape by removing the thumb from the top, the tube becomes filled immediately to the level of the water around it. In a goblet or basin pushed into water, with the mouth down- wards, the entrance of water is resisted for the like reason ; and if the goblet be inverted over a floating lighted taper, this will continue to float under it, and to burn in the contained air, however deep in the water it may be car- ried exhibiting the curious phenomenon of light below water, and being an emblem of the living inmate of a diving bell, which is merely a larger goblet holding. a man instead of a candle. GENERAL ATTRACTION. 25 "Mutual attraction" (See the Analysis, page 22.) Any visible mass of matter, then, as of metal, salt, sulphur, &c., we know to be really a collection of dust, or -minute atoms, by some cause made to cohere or cling together; yet there are no hooks connecting them, nor nails, nor glue ; and the connection may be broken a thousand times, by processes of nature or art, but is always ready to take place again ; the cause being no more destroyed in any case by interruption, than the weight of a thing is destroyed by frequent lifting from the ground. Now the cause we know not, but we call it attraction. The phenomena of attraction and its contrary, repulsion, particularly when occurring between bodies at consider- able distances from each other, are as inexplicable as any subjects which the human mind has to contemplate; but the manner or laws of the pheno- mena are now well understood. The general nature and extensive influence of attraction may be judged of from the following facts : Logs of wood floating in a pond, or ships in calm water, approach each other, and afterwards remain in contact. When the floating bodies are very small, or can approach very near to each other at the water's edge as glass bulbs in a tea-cup an additional force is called into play, as will be ex- plained unjer the head of " capillary attraction." l"he wreck of a ship, in a smooth sea after a storm, is often seen gathered into heaps. Two bullets or plummets suspended by strings near to each other, are found by the delicate test of the torsion balance (which will be described afterwards) to attract each other, and therefore not to hang quite perpen- dicularly. A plummet suspended near the side of a mountain inclines towards it, in a degree proportioned to its magnitude ; as was ascertained by the well- known trials of Dr. Maskelyne near the mountain Schehallion, in Scotland. And the reason why the plummet in such a case tends much more strongly towards the earth than towards the hill, is only that the earth is larger than the hill At New South Wales, which is situated on our globe nearly opposite to England, plummets hang and fall towards the centre of the globe, as they do here ; so that in respect to England, they are hanging and falling upwards, and the people there, like flies on the opposite side of a pane of glass, are standing with their feet towards us, hence called our antipodes. Weight, therefore, is merely general attraction acting everywhere. But it is owing to this general attraction that our earth itself is a globe : all its parts being drawn towards each other, that is, towards a common centre, the mass assumes the spherical or rounded form. And the moon also is round, and all the planets ; nay, the glorious sun, too, so much larger than these, is round ; suggesting the inference that all must at one time have been a certain degree fluid, and that all are subject to the same law. Descending again to the earth and observing minuter masses, we have many interesting instances of roundness from the same cause ; as the par- ticles of a mist or fog floating in air these, mutually attracting and coalescing into larger drops, and so forming rain dew-drops water trickling on a duck's wing the tear dropping from the cheek drops of laudanum glob- ules of mercury, like pure silver beads, coalescing when near, and forming larger ones melted lead allowed to rain down from an elevated sieve, and by 26 CONSTITUTION OP MASSES. cooling as it descends so as to retain the form of its liquid drops, becoming the spherical shot-lead of the sportsman, &c. The cause of this extraordinary phenomenon which we call attraction, acts at all distances. The moon, though 240,000 miles from the earth, by her attraction, raises the water of our ocean under her, and forms what we call the tide. The sun, still farther off, has a similar influence ; and when the sun and moon act in the same direction, we have the spring tides. The planets, so distant that they appear to us little wandering points in the heavens, yet, by their attraction, affect the motion of our earth in her orbit, quickening it when she is approaching them, retarding it when she is re- ceding. The attraction is greater the nearer the bodies are to each other as the light of a taper is more intense near to the taper than at a distance. A board of a foot square, represented in fig. 1 by A B at a certain distance from a light supposed at C, just shadows a board of two feet square, as E D, at double distance ; but a board with a side of two feet has four times as much surface as a board with a side of one foot, for it is not only twice as high or long, which would make it double, but twice as broad also, which Fig. 1. E * D makes it quadruple as a globe of two feet in diameter requires *just four times as much paper to cover it as a globe of one foot, and the corner, or fourth part E F, of the larger square here shown is just equal to the whole of the smaller square A B. Light, therefore, at double distance from its source, being spread over four times the space, has only one-fourth of the intensity; and for a similar reason, at thrice the distance it has only a ninth part, at four times a sixteenth part, and so on. Now light, heat, attraction, sound, and indeed every influence from a central point are found to decrease in the proportion here illustrated, viz., as the surface of squares which shadow one another increases. The technical expression is, " the intensity is in- versely as the squares of the distance ; (the distances being estimated from the centres of attraction or radiation) or one-fourth part as strong at double distance, four times as strong at half distance, and in a corresponding man- ner for all other distances. Accordingly, what weighs 1,000 Ibs. at the sea-shore, weighs five Iba. less at the top of a mountain of a certain height, or when raised in a balloon as is proved experimentally by a spring balance, or other means ; and at the distance of the moon, the weight, or force towards the earth, of 1,000 Ibs., is diminished to five ounces, as is proved by astronomical test. ATTRACTION has received different names as it is found acting under differ- ent circumstances. The chief distinctions are Gravitation, Cohesion, Capillary and Chemical attraction. Gravitation is the name given to it when acting at sensible distance, as in the cases of the moon lifting the tides the sun and earth attracting each COHESIVE ATTRACTION. 27 other a stone falling, &c. Most of the facts enumerated at page 25, belong to this head. Cohesion is the name given when it is acting at very short distances, as in keeping the atoms of a mass together., It might appear, at first sight, that it cannot be the same cause which draws a piece of iron to the earth with the moderate force called its weight, and which contains the constituent atoms of the iron in such strong cohesion ; but when we recollect that attraction is stronger as the substances are nearer to each other, the difficulty is met. Atoms very nearly in contact may be a million times nearer to each other than when only a quarter of an inch apart, aud therefore, when the heat among the atoms of any mass allows them to approach very near, they should attract mutually with great force. If, then, the surfaces of the bodies were not in general so very rough and irregular, that, when applied to each other, they can touch only in a few points of the million, perhaps, which each surface contains, bodies would be invariably sticking together or cohering by any accidental contact. The effect of artificially smoothing the touching surfaces is seen in the following examples : we may remark, however, that besides irregularity of surface, there is another ,reason, explained a little farther on, which prevents the cohesion. Similar portions being cut off with a clean knife from two leaden bullets, and the fresh surfaces being brought in contact with a slight turning pres- sure, the bullets cohere, almost as if they had been originally cast inone piece. Fresh-cut surfaces of India-rubber or caoutchouc, cohere in a similar way. We may hence make elastic air-tight tubes, by cutting off the edges of a strip of India-rubber and bringing the cut surfaces into contact by winding the strip spirally round any small rod or cylinder, and fixing it there for a time by tape or cord. Two pieces of perfectly smooth plate glass or marble, laid upon each other, adhere with great force : and so, indeed, do most well-polished flat surfaces. Cohesion between a solid and liquid, and between the particles of a liquid among themselves, is seen in the following instances : A flat piece of glass, balanced at the end of a weighing beam, and then allowed to come into contact with water, adheres to the water, and with much more force than the weight of water remaining upon it when again forcibly raised ! If there were not cohesion or attraction of the water par- ticles among themselves, as well as to the glass, the latter could only be held down by the weight of the water which directly adhered to it. In pouring water from a mug or bottle-lip, the water does not at once fall per- pendicular, but runs down along the inclined outside of the vessel ; chiefly in consequence of the attraction between this and the water; hence the dif- ficulty of pouring from a vessel which has not a projecting lip. The particles of water cohere among themselves in a degree which causes small needles gently laid on the surface to float : the weight of the needles is not sufficient to overcome the cohesion of the water surface. For the same reason, many light insects can walk upon the surface of water without being wetted. It is chiefly the different force of the attraction of cohesion in different 28 CONSTITUTION OF MASSES. liquids that causes their drops or gutts from the lip of a phial to be of differ- ent magnitude. Sixty drops of water fill the same measure as 10.0 drops of laudanum from a lip of the same size. In a larger mass of liquid, the attraction which, if acting alone, would draw the particles into the form of a distinct globe, yields to that which draws them towards the centre of the earth, and therefore the liquid assumes more or less completely, what is called the level surface, that is to say, a surface corresponding with the general surface of the earth. Attraction is called capillary when it acts between a liquid and the interior of a solid, which is tubular or porous. When an open glass tube is partially immersed in water, the water within it stands above the level of that on the outside ; and the difference of level is greater as the tube is less, because in small tubes, the glass all round being nearer to the raised water, attracts it more powerfully. Between the two plates of glass standing near to each other, with their lower edges in water, a similar rising of water will occur ; and if they are closer at one perpenificular edge than at the other, the surface of the sus- pended water will be higher there. The two plates of glass in such a case are found to be drawn towards each other by the interposed waters with a certain force, as happens also to glass beads, or other small bodies, floating in water with their surfaces so near to each other at the water's edge, that the water may rise between them, and the nearer they approach, the higher the water rises, and the more strongly it attracts. Water, ink, or oil, coming in contact with the edge of a book, is rapidly absorbed far inwards among the leaves. A piece of sponge or a lump of sugar touching water by its lowest corner, soon becomes moistened throughout. The wick of a lamp lifts the oil to supply the flame, from two or three inches below it. A mass of cotton thread hanging over the e.dge of a glass from the water within it, will empty it as a syphon would. A towel will empty a basin of water in the same way. Dry wedges of wood driven into a groove formed round a pillar of stone, on being moistened, will swell so as to rive off the portion from the block. In some portions of Germany, mill-stones are thus cut from the rock. An immense weight or mass suspended by a dry rope may be raised a little way, by merely wetting the rope; the moisture imbibed by capillary attraction in the substance of the rope causes it to swell laterally, and to become shorter. At one time, the small vessels of vegetables were supposed to raise the sap from the roots, by capillary attraction j but this is known now to be chiefly an action of vegetable life. Attraction has received the name of chemical attraction, or affinity, when it unites the atoms of two or more distinct substances into one perfect compound. There are about fifty substances in nature which appear, in the present state of science, distinct from each other, and are therefore called kinds of matter ; such as the various metals, sulphur, phosphorus, &c.; but whether these are in truth, originally and essentially different, or only one simple CAPILLARY ATTRACTION. 29 primordial matter, modified by circumstances as yet unknown to us, we cannot at present positively determine. Diamond and pure black carbon are the same substance only with different arrangement of atoms; and steel, which in the soft state the graver cuts as it would copper or silver, is exactly the same substance as when, after being tempered by heating and sudden cooling, it has become as hard nearly as diamond itself. Yet these differences are more striking than appear between some substances, which we now account essentially distinct. It is found, however, that the atoms of what we call different substances will not cohere and unite indifferently, to form masses, as atoms of the same kind do, there being singular preferences and dislikes among them, if it may be so expressed, or affinities, as the chemists term it : and when atoms of two kinds do combine, the resulting compound generally loses all resem- blance to either of the elements. Thus : Sulphuric acid will unite with copper and form a beautiful transcendent blue salt ; with iron it will form a green salt ; and if a piece of iron be thrown into a solution of the copper salt, the acid will immediately let fall the cop- per, and take up or dissolve the iron. Sulphuric acid will not unite with or dissolve gold at all. Quicksilver and sulphur unite in certain proportions and form the paint called vermillion ; in other proportions they form the black mass called Ethiops Mineral, Lead, with oxygen absorbed from the atmosphere or other source, forms what is called red lead, used by painters. Sea-sand, or flint and the substance called soda, when heated together, unite and form that most useful substance called glass. Certain proportions of sulphur and of iron combine and produce those beautiful cubes of pyrites or gold-like metal which are seen in slate. Chemical attraction operating thus, does not, in the slightest degree, interfere with general attraction or gravity, for every chemical compound weighs just as much as its elements taken separately. The history and classification of such facts connected with the combina- tions and analysis of different substances, constitute the science of chemistry, so attractive and so useful. It explains how the fifty kinds of matter above alluded to, by variously combining, form the endless diversity of bodies which constitute, as far as it has yet been explored, the mass of our ^lobe. The reasons of these various modifications of attraction are yet much hidden from us. It is a remarkable truth, that when different substances combine in the way now described, the proportions of the ingredients are always uniform, and such as to lead to the conclusion, that for every atom present, of one substance, there is exactly one, or two, or three, &c., of the other; so that, if there be ten atoms of one substance, there are exactly ten, or twenty, &c., of the other, but never an intermediate number, as 13 or 23 to 10, for then a particle of the compound would consist of one atom of the first, and of one and three-tenths, or two and three-tenths, &c., of the second substance, an absurdity if the atom be indivisible. For instance, a certain number of atoms of quicksilver, which weigh twenty-five grains, combine with a certain number of atoms of sulphur, weighing two grains, and form a black com- pound called Ethiops Mineral, or black sulphur of mercury ; and if a little more of either ingredients be added, it lies as a foreign mixture in the sul- phuret of mercury; but if just as much more sulphur be added as at first, so that there may be two atoms of it, instead of one, in every particle of the compound, a perfect combination of the whole will take place, and a new substance will appear, which we call vermilion. Many elementary substances 30 CONSTITUTION OF MASSES. will only unite with each other in one proportion, so that any two such sub- stances form only one compound ; but others unite in several proportions, so that several distinct compounds arise out of the same two elements. It thus appears, that although we do not know the exact number of atoms in a given quantity of any substance, whether, for instance, a grain of sulphuret of mercury has more or less than a million of them ; still, as. we know that in that grain there are just as many atoms of sulphur as of mer- cury, and that the weight of the whole sulphur to that of the whole mercury is as two to twenty-five, we know that the single atoms must have the same relation, or that the atom of mercury is 12 times as heavy as that of sulphur. Tables have been formed exhibiting the relative weights of the atoms of different substances ; and the number standing opposite to each substance is called its chemical equivalent, that is to say, the weight of its atom in relation to the weight of the atom of some other substance chosen as a standard. The equivalent of a compound substance depends, of course, both on the equivalents of the ingredients, and on the number of atoms existing in one integrant particle of the compound. There is no such thing as an atom of vermilion, or of any other compound, for the ultimate molecule or particle must contain at least one atom of the respective ingredients. The facts of the peculiarities and constancy of chemical unions are among the strongest arguments for the existence of similar ultimate atoms. Besides the simple cases of attraction now explained, there are two curious modifications, called electrical and magnetical attractions, which from their peculiarities are reserved for consideration in a future division of this work. " Atoms are more or less close, according to the quantity or REPULSION of heat among them; hence the forms of solid, fluid, air, &c." (Read the Analysis, p. 22.) Were there in the universe only atoms and attraction, as hitherto ex- plained, the whole material of creation would rush into close contact, forming one huge solid mass of stillness and death. But there is also heat or caloric, which counteracts attraction, and singularly modifies the results. It has been described by some as- a most subtle fluid, pervading all things, some- what as water pervades a sponge : others have accounted it merely a vibra- tion among the atoms. The truth is, that we know little more of heat as a cause of repulsion than of gravity as a cause of attraction ; but we can study and classify most accurately the phenomena of both. When a continued addition of heat is made to any body, it gradually increases the mutual distance of the constituent atoms, or dilates the. body. A solid thus is first enlarged and softened ; then melted or fused, that is to say, reduced to the state of liquid, as the cohesive attraction is overcome; and lastly, the atoms are repelled to still greater distances, so that the sub- stance is converted into elastic fluid or air. Abstraction of heat from such air causes return of states in the reverse order. Thus ice, when heated becomes water, and the water when farther heated becomes steam ; the steam when cooled again becomes water as before, and the water when cooled becomes ice. Ice, water and steam, therefore, are three forms or states of the same substance one of the most common in nature, being the material of the ocean. LIQUID AND AIR. 31 Other substances are similarly affected by heat, but as all have different relations to it, some requiring much for liquefaction, and some very little, we have that beautiful variety of solids, liquids and air, which constitutes four external nature. Dilitation. A rod of iron, which, when cold, will pass through a certain opening, and will lie lengthwise between two fixed points, when heated, be- comes too thick and to long to do either. For accurate mensuration, there- fore, rods or chains used as the measure, must either be at a given tempera- ture, or due allowance must be made for the difference. The walls of a building, under the pressure of a heavy roof, had begun to bulge out so as to threaten its stability. No force tried was sufficient to restore them to perpendicularity, until the idea occurred of using the con- tracting force of cooling iron. The opposite walls were then connected by a number of iron bars, passing through both, and having nuts to screw close to the wall upon their projecting ends, of which bars one-half were heated at a time, viz., every second or alternate bar, by lamps placed under them, and while lengthened in consequence, and projecting farther beyond the wall, their nuts were again screwed close up ; so that on cooling and con- tracting, they pulled the walls in a degree back to its place. The nuts of the second set of bars being then screwed home, the others were again heated, and advanced the object as much as the first; and so on, until the object was accomplished. The iron rim of a coach wheel, when heated, goes on loosely and easily, but when afterwards cooled, it binds the wheel most tightly, giving remark- able firmness and strength. Iron hoops on masts and casks, are made to bind in .a similar manner. The common thermometer for measuring degrees of heat, is a glass bulb, filled with mercury or other fluid, and having a narrow tube rising from it, into which the fluid, on being expanded by heat, ascends, and so marks the degree. A bladder not quite full of cold air, on being heated, becomes tense, and if weak, may even be burst. Liquid and Air. A piece of gold, lead, pitch, ice, sulphur, or of other thing, if sufficiently heated, melts or becomes liquid ; each substance, how- ever, requiring a different degree of heat gold requires 5,000 degrees, lead 600, ice, 32, and so forth ; and if the heating be afterwards continued, most things at certain higher temperatures suddenly expand again to many time the liquid volume, and becomes aeriform fluids. The conversion of water into steam is familiarly known to all. One pint of water driven off as steam from the boiler of a low-pressure steam-engine, fills a space of nearly 2,000 pints, and raises the piston through this, with a force of many thousands of pounds : it immediately afterwards appears again in the cold condenser as a pint of water. Six times as much heat is required to convert a pint of water into steam, as to raise it from an ordinary temperature to that of boiling but the steam, by occupying nearly 2,000 times the space -of the water, proves that heat merely produces a revulsion among the particles, and by no means fills up the interstices. The steam rising from boiling water does not appear to the thermometer hotter than the water itself; and hence it was that Dr. Black, whose genius shed so much light on this part of knowledge, gave the excess of heat the name of latent heat. The latent heat of common air is made sensible in the matcJi syringe. In this, which is close at the bottom, the piston Is driven down quickly and 32 CONSTITUTION OF MASSES. strongly, so as to compress very much the air which is underneath it, and the heat then condensed with the air is sufficiently intense to light a small piece of tinder attached to the bottom of the piston. Not only are spirits, aethers, oils, &c., convertible, as water is into aerifon* fluid, but also sulphur, phosphorus, mercury, and, indeed, all the metals and elementary substances ; some of them, however, requiring heats of great intensity. The varieties of form, then, in the bodies on the face of this earth, may be considered accidental, as dependent on the temperature of the earth, and do not mark the permanent nature ef the substances. In the planet Mercury, which is near the sun, resin, tallow, wax and many vegetable substances deemed by us naturally solid, would all be liquid, as oil is with us ; and a certain mixture of tin, zinc and lead, which with us is solid at common temperatures, but melts in boiling water, would there bo always liquid like our quicksilver. Our water, oils, and spirits, would there be in a state of steam or air, and could not be known as liquids, except by cooling processes and compression, such as we have lately teamed to use for reducing our different airs to the form of liquids. Again, in the cold planet Herschel, which is nineteen times farther from the sun than our earth is, water, if it exist, can be known only as rock crys- tal, which fire would have to melt as it does glass with us : our oils would be as .butter or resins, and quicksilver might be hammered as lead or silver is with us. On our own earth, near the equator, common sealing-wax will not retain impressions ; butter is oil in the day, and a soft solid at night ; and tallow candles cannot be used. And near our pole, in winter, the quicksilver from a broken thermometer is solid metal ; water must be melted by fire for use ; oils are solid, &c. To judge, then, of the constitution of nature aright, we must always take extended surveys, and not allow prejudice to mislead us, as it did that Eastern potentate, who put a traveller to death for saying he had visited remote northern countries, where water was sometimes to be seen solid like crystal, and sometimes white and fleecy, like feathers. The ancients believed that there were just four elements concerned informing our globe, with all upon it, viz., earth, water y air and fire. What a contrast between former and present knowledge ! Repulsion without sensible Seat. As we stated in a former paragraph that besides general attraction, under names gravitation, cohesion, capillary and chemical attraction, there are modifications which have the names of electrical and magnetical attractions ; so we nave now to remark, that, besides the general repulsion of heat just described, there are peculiarities which we call electrical and magnetical re- pulsions. Whether these depend altogether on different causes, or are only modifications of effect from the- same cause, we cannot yet positively decide. And it is a curious fact connected with the subject, that there seems to be a film of repulsion, so to express it, covering the general surfaces of all bodies, and preventing their meeting in absolute contact, even when they appear to the human eye so to meet. Were it not for this, things would be constantly approaching so closely to each other, that they would stick or cohere, in a way to disturb the common operations of nature. The following facts illus- trate this superficial repulsion, and the means which art uses to overcome it for particular purposes. REPULSION OP SURFACES. 33 Newton found that a ball of glass, or a watch-glass, laid upon a flat surface of glass does not really touch it and cannot be made to touch it by a force of even 1,000 pounds to the inch. In like manner, when glass, stone, porcelain, or indeed almost any body is broken, we cannot make the parts cohere again by simply pushing them together in their former position. Where a union, therefore, between sepa- rate masses is desired, we are compelled to have recourse to various artifices A few cases in which cohesion is easily affected, were enumerated at page 27 : the following are other instances of a different kind. Gold leaf laid upon clean steel, and then forciby struck by a hammer, coheres to the steel, and gilds it permanently. But iron can be made to cohere to iron, only by rendering both pieces red hot before hammering : the process is called welding. Iron and platinum are the only metals that can be welded. Tin and lead, in sheets, pressed together between the strong rollers of a flatting-mill, cohere. The other metals require to be melted before the superficial repulsion gives way so as to allow separate quantities to cohere or run into one mass. It is thus, for instance, that gold, silver, lead, &c., are treated. In many cases the substances are not such as can be melted, (wood or marble, for instance,) and then it is necessary to use some soft glue or cement. Cements must have strong attraction for both substances, and, when dry or cool, must be tenacious in themselves ; solder, paste, common glue, motar, &c., are the principal substances of this kind. " Certain modifications of attraction produce the subordinate states, called crystal, porous, dense, &c" (Read the Analysis, page 22.) " It is a remarkable circumstance, that attraction, in causing the atoms to cohere so as to form solid masses, seems not to act equally all around each atom, but between certain sides or parts of one, and corresponding parts of the adjoining one; so that when atoms are allowed to cohere according to their natural tendencies, they always assume a certain regular arrangement and form, which we call crystalline. Because in this circumstance they seem to resemble magnets, which attract each other only by their poles, the fact has been called the polarity of atoms. It is the cause of several of the peculiarities above enumerated, as elasticity, &c. " Crystallization" is exemplified in the following particulars : Water beginning to freeze, shoots delicate needles across the surface ; these thicken and interweave until the whole mass has become solid, but the crystalline arrangement always remains. In most substances, this arrangement is remarkably proved, by the forms of the surfaces left, when the mass is broken. Moisture, freezing on the window-pane in winter, exhibits a beautiful variety of arborescence. A flake of snow viewed in the microscope, is seen to be as symmetrically formed as a fern-leaf or a swan's feather. If a piece of copper be thrown into a solution of silver in nitric acid, it is preferred by the acid to silver, and is dissolved accordingly : the silver in the mean time, during its precipitation or separation, assumes the form of a singularly beautiful shrub or tree, resting on the remaining copper as its root. This appearance is call the arbor Diande. 3 34 CONSTITUTION OF MASSES. Any metal which has been melted, when allowed to cool again, slowly and at rest, becomes solid first on the outside of the mass. If, before the cooling be completed, the remaining liquid be poured from within, a curious internal crystalline structure, like grotto work, is seen. What is called the grain of a metal is the result of this crystallization. Saltpetre, glaubler salt, copperas (to use popular names,) or any other of the many neutral salts, being dissolved in water, and the water being then allowed slowly to evaporate, reappears in beautiful regular crystals, each salt having its peculiar forms, bounded by perfectly plane and polished surfaces. If any such crystal be broken in any part, the broken surface appears to the microscope as if regular layers of particles had been disturbed, (as we see on a larger scale in a broken stack of bricks, or broken pile of shot in a battery yard,) and the defect of the crystal will be exactly filled up by replacing it in the evaporating solution proving that the ultimate particles are all of the same size. All the precious stones are crystals, and can be well cut only parallel to their natural surfaces. The basaltic pillars of the Giant's Causeway in Ireland, and of the Isle of Staffa, which appears like a garden supported on magnificent columns in the midst of the ocean, are natural crystalline arrangements of particles, equalling in regularity and beauty any human work, and in granduer so far surpassing even the Egyptian pyramaids, that superstitious conjecture naturally supposed them the work of giant architects. It would be endless to go on enumerating crystalline masses, for nature's forms generally, in the inanimate creation, as well as in organized bodies, are regular and symmetrical ; and what we see on earth of broken conti- nents, and islands, and rocks, and wild Alpine scenery, are the effects of subsequent convulsions, which have deranged a primitive and natural order. Much ingenuity has been employed to account for the specific forms which different crystalline bodies assume; but the subject is not yet reduced to a state fitting it to be a part of this elementary study. A familiarity with the various figures which the exact science of measures treats of, is required in the person who expects to pursue it with pleasure or advantage. The facts are extremely curious, and the scientific investigation of them may ultimately give important information respecting the intimate consti- tution of material nature. " Porous." The crossing of the constituent crystalline needles or plates in bodies, causes them to be porous or full of small vacant spaces. In some cases these are visible to the eye, in many more cases, they are visible to the microscope, and in all, they are to be proved in some way. Owing to the porosity arising from the new arrangement of atoms of solidifying, water and a very few other substances become more bulky in the change from the liquid to the solid state. Water then dilates with such force as to burst the strongest vessels which art can provide, and in winter to split even rocks, where it has been retained in their crevices ; freezing water thus curiously producing effects which surpass those of exploding gunpowder. This agency of water contributes to the gradual breaking down of our Alpine summits, and the falling of their destructive fragments into the valleys. The stone called hydrophane (agate) is opaque, until dipped into water, when it absorbs into its pores one-sixth of its weight of the water, and after- wards gives passage to light. Into crystallized sugar, and various stones, much water will enter without increasing the bulk. DENSITY. 35 * A kind of sandstone, suitably shaped, forms an excellent filter or strainer for water. Pressure will force water through the pores of the most solid gold : as was seen in the famous Florentine experiment, where a hollow, thick, golden ball, being filled with water and squeezed^ to try the compressibility of water, was found to perspire all over. The examples of porosity in animal and vegetable bodies, are, however, the most remarkable. Bone is a tissue of cells and partitions, as little solid as a heap of empty packing-boxes. Wood is a congeries of parallel tubes, like bundles of organ pipes. It has lately been proposed to prepare wood for certain purposes, as for making the great wooden pins or nails used in ship-building, by squeezing it to half its lateral bulk between very strong rollers, and thus making its density approach to that of metal. A piece of wood sunk to a great depth in the ocean, and exposed to the pressure there, has its pores soon filled with water, and becomes nearly as heavy as stone. Thus it was with the boat of a whale-fishing ship, which had been dragged far under water by a whale, and which, on being afterwards drawn up, was supposed by the crew to be bringing a piece of rock with it. A piece of cork in a strong, close glass vessel, nearly full of water, may be seen floating at the top ; but if more water be then forcibly pumped into the vessel, the cork will be squeezed and reduced in size, until at last it be- comes heavier than water, and sinks. On water being afterwards allowed to escape, the cork will resume its bulk and will rise. A cork sunk 200 feet under water will never rise again of itself. A bottle of fresh water, corked and let down thirty or forty feet into the sea, often comes up again with the water saltish, although the cork be still in its place: the explanation being, that the cork, when far down, is" so squeezed as to allow the water to pass in or out by its sides, but on rising, resumes its former size. " Density" or the quantity of atoms which exist in a given space, is very different in different substances. A cubic inch of lead is forty times heavier than the same bulk of cork Mercury is nearly fourteen times heavier than an equal bulk of water. The density must depend on, first, the size or weight of the individual atoms ; secondly, the degree of porosity just now explained; and thirdly, the proximity of the atoms in the more solid parts which stand between the pores. From many circumstances it appears, that the atoms even of the most solid bodies are nowhere in actual contact, but are retained in their places by a balance between attraction and repulsion thus, A body dilates or contracts, according as heat is added or taken away from it. A weight placed on any upright rod or pillar, shortens it and lessens its bulk, and if suspended from the bottom, lengthens it and increases its bulk, the .rod in both cases returning to its former dimensions when the weight is removed. When a plank or rod is bent, the atoms on the concave side are, for the time, approximated, and those on the convex side are drawn more apart. It is remarkable in solid bodies, not only how precisely the balance between 36 CONSTITUTION OF MASSES. attraction and repulsion determines the relative position of the particles, but also how strongly ; for any farther separation of the particles is resisted by all the force which we call the tenacity or cohesion of the substance, and any nearer approach by all the force which we call the hardness or incom- pressibility. Tin and copper, when melted together, to form bronze, occupy less space by one-fifteenth than when separate : proving that the atoms of the one are partially received into what were vacant spaces in the other. A similar con- densation is observed in many other mixtures. A pound of water and a pound of salt, when mixed, form two pounds of brine, but which has much less bulk than the ingredients apart. So also of a pound of sugar dissolved in a pound of water. Water and liquids generally resist compression very powerfully, but yield enough to show that the particles are not in contact. It is found that at 1,000 fathoms down in the sea the water is compressed by the superincum- bent water so as to have bulk about a hundredth part less than it would have at the surface. In aeriform masses the atoms are very distant, and hence the masses are more easily compressed. A pint of water, on assuming the aeriform state, in which it is called steam, under ordinary pressure, acquires nearly 2,000 times its former bulk. A hundred pints of common air may be compressed into a pint vessel, as in the chamber of an air-gun ; and if the pressure be much farther increased, the atoms will at last collapse and form a liquid. The heat which was contained in such air, and gave it its form, is squeezed out in this operation, and becomes sensible all around. From these proofs of the non-contact of the atoms, even in the most solid parts of bodies ; from the very great space obviously occupied by pores the mass often having no more solidity than a heap of empty boxes, of which the apparently solid parts may still be as porous in a second degree, and so on ; and from the great readiness with which light passes in all directions through dense bodies like glass, rock crystal, diamond, &c., it has been argued that there is so exceedingly little of really solid matter, even in the densest mass, that the whole world, if the atoms could be brought into absolute contact, might be received into a nut-shell. We have as yet no means of determining exactly what relation this idea has to truth. The comparative weights of equal l>ulk$ of different bodies are called their specific gravities. In thus comparing bodies, it was necessary to choqse a standard ; and water, as being the substance most easily procurable at all times and in all places, has been generally adopted. The metal called platinum, the heaviest of known substances, is about twenty-two times as heavy as an equal bulk of water, and is therefore said to have specific gravity of 22 gold is nineteen times as heavy mercury thirteen and a half lead eleven iron eight and a half copper eight com- mon stones about two and a half woods from half to one and a half cork one-quarter, &c. " Hardness" is not proportioned, as might be expected, to the density of the different bodies, but to the polarity of the atoms in them, that is, to the force with which the atoms hold their places in some particular arrangement. Hardness is measured generally by the circumstance of one body being DENSITY. 37 capable of scratching another. It is here worthy of notice, however, that the powder or dust of a softer body will often, through an effect of motion to be described below, aid in wearing down or polishing one that is harder. Gold, though soft, is four times heavier than the hard diamond; and mercury, which is fluid, is nearly twice as dense as the hardest steel. Diamond is the hardest of known substances. It cuts or scratches every other body, and is generally polished by means of its own dust. Glass-cutters use a point of diamond as a glass-knife, for dividing and shaping their panes. Common flint also cuts glass, as is proved by the frequent scribblings on windows. It is remarkable, that the preparation of iron, called steel, may either be soft like pure iron, or from being heated and suddenly cooled, in the process called tempering, may become nearly as hard as diamond. The discovery of this fact is, perhaps, second in importance to few discoveries which man has made ; for it has given him all the edge tools and cutting instruments by which he now moulds every other substance to his wishes. A savage will work for twelve months, with fire and sharp stones, to fell a great tree, and to give it the shape of a canoe ; where a modern carpenter, with his tools, could accomplish the object in a day or two. The project has lately been realized, of engraving on plates of soft steel, instead of copper, and afterwards tempering the steel to such hardness, that it may be used as a type or die to make its impression, not on paper, but on other plates of soft steel or of copper ; each of which then is equal in value to an original and distinct engraving. By this means the beautiful produc- tions of art, instead of being limited to a comparatively small number of copies and of persons, may be multiplied almost to infinity, becoming the cheap delight of all. " Elasticity" is present in a mass when the atoms, cohering in a particular arrangement only, yield, however, to a certain extent, when force is applied, but move back or regain their natural positions on the force being with- drawn. Elastic bodies vary much as to the extent to which they yield without breaking, and as to the degree of perfection with which, after the bending, or displacement of atoms, they regain their former state. India rubber is extensively elastic, for it yields far ; but it is not perfectly elastic, for when stretched much or often, it becomes perfectly elongated. Glass, again, is perfectly elastic, for it will retain no permanent bend; but, unless in very thin plates indeed, or in fine threads, it will not bend far without breaking. All hard bodies are elastic, as steel, glass, ivory, &c., and many soft ones, as caoutchouc, silk, a harp string, &c. The aeriform bodies are all per- fectly elastic, as is rudely seen in a bladder filled with air, when squeezed, and allowed to expand again ; and they will change volume to a very great extent. Liquids also are perfectly elastic, but to a small extent. A good steel sword may be bent until its ends meet, and yet, when allowed, will return to perfect straightness. A rod of bad steel, or of other metal, will be broken in bending, or will retain a bend. An ivory ball, let fall on a marble slab, rebounds, owing to the great elasticity of both bodies, nearly to the height from which it fell, and no mark is left on either. If the slab be wet, it is seen that the ivory or mar- 38 CONSTITUTION OF MASSES. ble, or both, had yielded considerably at the point of contact, for a circular surface of some extent on the slab is found dried by the blow. The sudden expulsion of air from between the meeting surfaces might contribute to the effect, but the result is very nearly the same when the experiment is made in a vacuum. Billiard balls scarcely lose even their polish by long wear, although the touching parts yield at every stroke. A marble chimney-piece, long supported by its ends, is found at last to be bent downwards in the middle ; and the bend is permanent. A steel watch-spring, although so much and so constantly bent, resumes its original form when freed at the end of a century ; but occasionally, without evident cause, while in action, it will suddenly give way. Elasticity is a property of bodies of great utility to man, as in his time- pieces, carriage-springs, gun-locks, &c., &c. " Britileness" designates that constitution of a body where, with hardness, and elasticity perfect as far as it goes, the cohesion among the atoms exists within such narrow limits that a very slight change of position or increase of distance among them is sufficient to produce a rupture. A compara- tively slight force, therefore, if sudden, breaks them. It belongs to most very hard bodies. Glass scratches an iron hammer, proving that it is harder than iron yet glass is the very type of fragility j yielding to the stroke of soft wood, or, indeed, of almost any thing which can give a blow. Steel, when tempered so as to be very hard, becomes brittle also. The steel chisels and tools with which artificers now shape the stones and metals as they formerly did wood, require, of course, to be exceedingly hard ; but they thereby lose in regard to the extent of their elasticity, and hence are frequently broken. Cast iron, which is much harder than malleable or wrought iron, is very brittle, while soft iron and steel are the toughest things in nature. " Malleable" or reducible into thin plates or leaves by hammering. This property, in opposition to elasticity and brittleness, belongs to bodies whose atoms cohere equally in whatever relative situations they happen to be, and therefore yield to force, and shift about among each other, with- out fracture or change of property, almost like the atoms of a fluid. Gold is remarkably malleable, for it may be reduced to leaves of the thin- ness of 360,000 to the inch, or of 1,800 to a sheet of common paper. For gold-beaters the metal is first formed into rods, these are ^afterwards rolled or battened into ribbons ; the ribbon is cut into portions, which are extended, by hammering, to great breadth and thinness, and which being again divi- ded into portions, are hammered and extended to the thinness described. Silver, copper and tin may also be hammered until very thin. Most other metals crack or are torn before the operation is carried far ; and some, on being struck, are broken at once, almost like glass. tl Ductile" or susceptible of being drawn into wire. One might expect malleability and ductility to belong to the same substances and in the same degrees but they do not. In ductile substances, as in malleable, the atoms seem to have no more fixed relation of position than in a liquid, but yet they cohere very strongly. One end of a rod of iron, or other ductile metal, being reduced in size so DENSITY. 39 as to pass through an opening in a plate of steel, is seized by strong nippers on the other side of the plate, and the whole rod is drawn through. It is thus reduced, of course, to the size of the opening, and is lengthened in a like proportion. By repeating the operation through smaller holes succes- sively, a wire may at last be obtained to the size of a hair. Dr. Wollaston's ingenuity produced platinum wire finer than spider's thread. He filled a space in the axis of a silver wire with small platinum wire. He then drew or reduced the compound piece to the smallest wire possible, and on dissolving the silver from the outside, he exposed to view the delicate filament of platinum. The order in which metals may be ranged according to their ductility is, platinum, silver, iron, copper, gold, &c. Melted glass has great ductility. The workers draw or spin it into threads by merely attaching a point, pulled out from the mass, to the circumference of a turning-wheel. A uniform thread then continues to be drawn out and wound upon the wheel, at a rate of 1,000 yards or more per hour. This glass thread, when lying together in quantities, resembles beautiful white hair, and when cut in bunches, it serves as an ornament to the female head, waving in the air like the delicate plume of a bird of paradise. "Pliant." In bodies distinguished by this title, the cohesion is not des- troyed by considerable change of direction among the particles, but there is little elasticity, and unlike what happens in a ductile mass, the same atoms always remain together. Of all pliant things, the chief are animal and vegetable fibres and mem- branes as silk, bladder, lint, hemp, &c., &c. " Tenacity" means the force of cohesion among the atoms of any mass. It belongs more or less to all solids, and even to liquids. This property varies much in different substances. Iron and its modifica- tion called steel possess it in the most remarkable degree. The following table shows the comparative tenacity, or strength to resist pulling of certain metals and woods. Supposing similar wires or rods of each to be used, and of such a size that the surface of a broken end or cross- section would be the one-thousandth of a square inch, the weights supported would be nearly as follows : METALS. Cast Steel . . .134 Ibs. Best wrought iron . 70 Cast Iron . ....... . 19 Copper .",.,- .,- : .1-.^ 19 Platinum . . -^ , 16 Silver . , ; . ^ 11 Gold . . ;;:; " 9 Tin . :,./.,. 5 Lead . : V.^>: 2 WOODS. Teak . . ',13 oak . .-;' .:.' 12 Beech . . . 12* Ash . . :$ . 14 Deal S. 11 40 CONSTITUTION OF MASSES. Iron compared in this way, is five or six times stronger than oak. Steel wire will support about 39,000 feet, that is, 7? miles of its own length. Certain animal substances have great tenacity; as the silk-worm's thread, which is our strongest connecting or sewing material, and has such flexibility united with its strength the ligaments and tendons of the animal body, pos- sessing at once such admirable strength, elasticity and pliancy : these when dried, and otherwise prepared, constituted the tough bow-strings of our re- mote forefathers the hair or wool of animals twisted into threads, and worked into strong and beautiful textures of the loom strips of animal in- testines prepared and twisted, forming the cords of harp and violin, and in strength and uniformity rivaling the steel wires of keyed instruments. The gradual discovery of substances possessed of strong tenacity and which man could yet easily mould to his purposes, has been of great importance to his progress in the arts of life. The place of the hempen cordage of Euro- pean navies is still held in China by twisted canes and strips of bamboo ; and even the hempen cable of Europe, so great an improvement on former usage is now rapidly giving way to the more complete and commodious secu- rity of the iron chain of which the material to our remote ancestors existed only as a useless stone or earth. And what a magnificent spectacle is it, at the present day, to behold chains of tough iron stretched high across a chan- nel of the ocean, as at the Menai Strait, between Anglesea and England, and supporting there an admirable bridge-road of safety along which crowded processions may pour, regardless of the deep below, or of the storm ; while under it, ships with full sails spread pursue their course, uninolesting and unmolested ! APPENDIX TO PART I. SECTION I BY THE AMERICAN EDITOR. Ir the reader has studied the preceding section with attention he is prepared to understand the following propositions. Prop. 1 Matter is endowed with properties. Prop. 2. The properties of matter are distinguishable into two classes, first, those which are general or belong to all kinds of matter, and second, those which tare peculiar or belong only to particular kinds of matter. Prop. 3. The general properties of matter are, indestructibility (p. 22;) extension or the property of occupying a portion of space (jp. 24; ) divisi- bility (p. 23 ;) impenetrability (p. 24; ) and inertia, (p. 42. ) Prop. 4. Every particle of matter, and also all masses, have a mutual attraction for one another, or endeavor to get near each other ; and this attraction is inversely as the squares of the distances. Attractions may be primarily distributed into two classes : one consisting of those which exist between the molecules or constituent parts of bodies, and the other between the bodies themselves. The former are called mole- cular or atomic attractions, the latter gravitation (p. 26 : ) of the former there are several varieties, 1st, cohesion (p. 27;) when this variety of molecular attraction is exhibited by liquids pervading the interstices of porous bodies, ascending in crevices or in the pores of small tubes, it is called ca- pilliary attraction (p. 28. ) The other varieties of molecular attractions are affinity or chemical attraction (p. 28, ) and electric and magnetic attrac- tion, (p. 30. ) Prop. 5. Attraction of gravitation, or that force by which all the masses of matter tend towards each other, is exerted at all distances. Prop. 6. Attraction of cohesion acts only within certain limits, and where its sphere of attraction ends, a repulsive force begins. Prop. 7. Repulsion, except when dependent on electricity or magnetism, is owing to the presence of heat, which latter pervades all matter. Prop. 8. The particles of matter are more or less close, according to the quantity of heat among them ; but they are never in actual contact (p. 30- 31,) and hence porosity is usually considered as one of the properties of matter. Prop. 9. The peculiar properties of matter are density (p. 35, ) hardness (p. 36, ) elasticity (p. 37, ) brittleness (p. 38, ) malleability (p. 38, ) duc- tility (p. 38, ) pliability (p. 39, ) tenacity, (p. 39, ) &c. 42 MOTIONS AND FORCES. SECTION II. THE MOTION OR PHENOMENA OF THE UNIVERSE.* ANALYSIS OF THE SECTION. The bodies or masses composing the universe may be at rest or in motion, and to change any present state, force proportioned to the quantity of the body and to the degree of change, is equally required, whether to give motion, to take it away, or to bend it : a truth expressed by saying that matter has INERTIA, or figuratively, a stubbornness. Uniform straight motion, then, is as naturally permanent as rest. And the motion in any body, measured by its velocity, quantity of matter and direction, is the measure of the amount and direction of any single force or of any com- bination of forces, which has produced it, as also of the force or momen- tum which the body can exhibit again when opposed or made to act itself as a cause of some new motion. The great forces of nature, referred to by the two words ATTRACTION and REPULSION, acting upon INERT matter, produce the equable, accelerated, retarded and bent motions which constitute the great phenomena of the universe. Tides, currents, winds, falling bodies, &c., exemplify attrac- tion. Explosion, steam collision, &c., exemplify repulsion. And as in every case of attraction or repulsion two masses at least must be con- cerned, there is no motion or action in the universe, without an equal and opposite motion or re-action. Motion" Is the term applied to the phenomenon of the changing of place among bodies. Were there no motion in the universe it would be dead. It would be without the rising or setting sun, or river flow, or moving winds, or sound, or light, or animal existence. To understand the nature and laws of the motions or changes which are going on around him, is to man of the greatest importance, as it enables him to adapt his actions to what is coming in futurity, and often to interfere so as to control futurity for his special purposes. Motion, in any particular case, is described by referring to certain objects to mark place, and to some other motion chosen as the standard of velocity. A man sitting on the deck of a sailing ship, has common motion with the ship : if walking on the deck, he has relative motion to the ship : but if he be walking towards the stern, just as fast as the ship advances, he is at rest relatively to the bottom or shore. A ship sailing against the tide, just as fast as the tide runs, is as much at rest relatively both to the earth and water as if she were at anchor. Absolute motion is that which is rela- tive to the whole universe, or rather to the space in which the universe ex- ists. We have no means of ascertaining such : for although we know how fast our globe whirls upon its axis and wheels round the sun, we have no measure of the motion of the sun himself revolving possibly round some * The reader should here re-peruse the title and Analysis at page 22. MOTION. 43 more distant centre, but almost certainly having a progress in space, and carrying all the planets along with him. Motion is called rapid, as that of lightning slow, as that of the sun-dial shadow ; both terms have reference to the ordinary intermediate velocities observed upon earth. It is called straight or rectilineal, in the apparent path of a failing body bent, or curvilinear, in the track of a body thrown obliquely accelerated, in a stone falling to the earth retarded, in a stone thrown upwards while rising to the point where it stops before again descending. " Owing to the INERTIA of bodies, force is equally required to impart motion and to take it away." (Read again the last Analysis.) If a man put his hand to the crank of a heavy fly-wheel or grindstone, to turn it, he experiences a certain resistance, which, however, gradually yields to his effort, and he leaves the wheel whirling with velocity proportioned to the effort. If he then puts out his hand again to stop the wheel, he experi- ences an opposite but similar resistance, which however, as before, gradually yields, and he brings the wheel to rest. In the second case the effort re- quired of him is less than the first, by reason of the friction of the turning axle, and the resistance of the air in which the wheel moves, obstructions which, when he was giving motion, opposed him, but when taking it away assisted him. That these obstructions caused the whole difference in such a case, and that they are the great reasons why all ordinary motions on earth seem to tend of themselves to cease, will be shown in subsequent pages. It is the resistance overcome in moving the wheel or in stopping it, and occa- sioning an expenditure of force proportioned to the mass and to the degree of change of state, which is called the INERTIA of the mass, or the vis iner- tias, and sometimes, to help the conception of the student, the stubbornness, sluggishness, or inactivity; but none of these words can originally suggest to the mind all that is intended to be conveyed. An exact measure of the amount of inertia is contained in the familiar fact that a body let fall near the surface of the earth, falls rather more than 16 feet in the first second of time, the well-known weight of the body, or force of terrestrial attraction acting upon it for one second, being just suffi- cient to overcome its inertia to the extent stated. Were the inertia of matter only half of what it is, a body near the earth would fall 32 feet in the second, instead of 16, as it equally would, if, with present inertia, the attraction of the earth were doubled. And were there no inertia, it would fall or pass through any height, however great, in one instant. As the amount of inertia thus determines the amount of other force required to give motion to a mass, so does it determine the amount of force required to destroy motion in a mass. A heavy cannon-ball, if wanting inertia, might be dispatched with the speed of lightning by the slightest force, but then the stiffness of a stalk of corn would suffice to arrest it ; and while the ball, with the inertia now existing, takes the force of pounds of gunpowder to give it its usual motion, it may not be stopped, even by the cohesion of a block of granite, which accordingly it shivers to pieces. The numerous examples now to follow will prove the immense importance of inertia in the general opera- tions of nature. When the sails of a ship are first spread to receive the force or impulse of the wind, the vessel does not acquire her full speed at once, but slowly, as the continuing force gradually overcomes the inertia of her mass. When the 44 MOTIONS AND FORCES. sails are afterwards taken in, she does not loose her motion at once, but slowly again, as the continued resisting force of the water destroys it. Horses must make a greater effort at first to put a carriage in motion than to maintain the motion afterwards. And a strong effort is required to stop a moving carriage. When a carriage, of which the body hangs from springs, is first moved, the body appears to fall back, and a person within seems to be suddenly forced against the back cushion. When the carriage is stopped again the body swings forward, and if the stoppage be very sudden, a care- less passenger may unwittingly pop his head through a front glass. These particulars prove the inertia, first of rest, and secondly of motion. A man standing carelessly at the stern of a boat, when the boat begins to move, falls into the water behind ; because his feet are pulled forward while the inertia of his body keeps it where it was, and therefore behind its sup- port. The stopping of a boat, again, illustrates the opposite inertia of motion, by the man's falling forward. An awkward rider on horsback may be left behind, when his horse starts forward suddenly : or may be thrown off on one side by the horse starting to the other. A horse at speed, stopping suddenly, often sends his cavalier over his ears as was mortifyingly experienced by a coxcomb, who, on an old cavalry horse, chose to canter along a foot-path, to the annoyance of the company, and whose horse on hearing the word halt loudly addressed to it by a waggish officer of the regiment, who happened to be there and to recog- nize it, suddenly stood and got rid of its load. The mind or will of the beau had sinned against the law of propriety, but his body very perfectly obeyed the laws of inertia and gravity, by shooting forward in a parabolic curve to the earth. A young man not yet accustomed to the whip, drove his phaeton against a heavy coach on the road, and then to his father foolishly excused his awk- wardness, in a way which led to the prosecution of the coachman for furious driving. At the trial, the youth and the servant both deposed that the shock of the coach was such as to throw them over their horses' heads, and thus lost the case, by unconsciously proving, that the faulty velocity was their own. A man jumping from a carriage at speed is in great danger of falling for- ward, when his feet reach the ground ; for his body has as much forward velocity as if he bad been running with the speed of the carriage and unless he advance his feet like a running man, to support his advancing body, he must as certainly be dashed to the ground, as a runner whose feet are sud- denly arrested. A man racing who receives a signal to stop, and a man jumping from a flying vehicle, must check their motion^ nearly in the same way. A person wishing to leap over'a ditch or chasm, first makes a run, that the motion thereby acquired may help him over. A standing leap falls much short of a running one. An African traveller saw himself pursued by a tiger, from which he could not escape by running ; but perceiving that the animal was watching an opportunity to seize him by its usual spring or leap, he artfully led it to where the plain terminated in a precipice hidden by brush-wood, and he had just time to transfer his hat and cloak to a bush, and to retreat a few paces when the tiger sprung upon the bush, and by the moral inertia of its body, was carried over the precipice and destroyed. From a glass of water suddenly pushed forward on the table, the water is spilt or left behind \ but if the glass be already in motion, as when carried MOTION. 45 by a person Balking, and if it then be suddenly stopped by coming against an impediment, the water is thrown or spilt forward. A servant carrying a tray of glasses or china in the dark, and coming sud- denly against an obstacle, hears all his freight slipping forward and crashing at his feet : and a too hurried departure with such a load causes equal des- truction, on the opposite side. The actions of beating a coat or carpet with a cane, to expel the dust ; of shaking the snow from one's shoes, by kicking against a door-post ; of clean- ing a dusty book by knocking it against a table, or shutting it violently all illustrate the same principle. If a guinea be laid on a card which is already balanced on the point of the finger, a small fillip or blow to the edge of the card will cause it to dart off, but the guinea, owing to its inertia, will remain resting on the finger, its inertia being greater than the friction on it of the card passing from under- neath it. When we desire a person, with suspected disease of the brain, to shake his head and tell whether and where he feels pain, we are doing nearly as if we touched the naked brain with the finger to find the tender part ; for the inertia of the brain, when the skull is moved, causes a momentary pres- sure between it and the skull, almost equivalent, for the purpose desired, to such a touch. This kind of pressure is sufficient to break and destroy tender wares as glass or eggs in packages which are too suddenly moved or stopped. A weight suspended by a spring on ship-board is seen vibrating up and down as the ship pitches with the waves. It seems to fall as the ship rises, and to rise as the ship falls : but the motion is really in the ship, and the comparative rest is in the weight. A heavy weight so supported, and con- nected with a pump-rod, would work the pump. Like the weight last mentioned, the mercury ofa common barometer on ship-board is seen rising and falling in the tube; and until the important improvement was lately made, of narrowing one part of the tube to prevent this, the mercurial Barometer was useless at sea. The explanation is, that the tube rises and falls with the ship, from being connected with it ; but the mercury, which plays freely in the tube, and is supported by the atmospheric pressure, tends, by its inertia, to remain at rest, and thus makes the motion of the ship apparent. What happens to the mercury in the barometer-tube on ship-board, indi- cates what happens to the blood in the vessels of animals under similar cir- cumstances. In any long vein below the heart, when the body falls, the blood, by its inertia and the supporting action of the vessels, does not fall so fast, and therefore really rises in the vein : and as there are valves in the veins preventing return, the circulation is thus quickened without any mus- cular exhaustion on the part of the individual. This helps to explain the effect of the movement of carriages, of vessels at sea, of swings, &c., and of passive exercise generally, on the circulation, and leaves it less a mystery why these means are often so useful in certain states of weak health. If a cannon ball were to break to pieces in its flight, its parts would still advance with the previous velocity. And thus, in the deadly contrivance of the Shrapnell-shell, which is in a case containing hundreds of musket bul- lets, when these are scattered at the desired distance from the devoted body of men, they retain the forward velocity of the shell, and spread death around like the near discharge of a whole battalion of musketry. On the awful occasion of a ship in rapid motion being suddenly arrested 46 MOTIONS AND FORCES. by a sunken rock, all things on board, men, guns, and furniture, start from their places and dash forwards ; while the onward inertia or moral obstinacy of the hinder parts of the ship, suffices to crush her bow against the rock. " Motion as naturally permanent as rest." From the instances now given, it is seen that a body at rest would never move if force were not applied, and that a body put in motion retains mo- tion, at least for a time, after the force has ceased; but there is a feeling from common experience, that motion is an unnatural or forced state of bodies, and that all moving things, if left to themselves, would gradually come to rest. It is recollected that a stone projected comes to rest, or a wheel left moving, or a bowl rolled on the green, or the waves heaving after "a storm and in a word, that there is no perpetual motion on the earth. On more attentive consideration, however, it may be perceived that there are prodigious differences in the duration of motions, and that the differences are always exactly proportioned to evident causes of retardation, and chiefly to friction and the resistance of the air. Friction is the resistance which bodies experience when rubbing or sliding upon each other; and however much it may be diminished by art, it can in no case be annihilated. Air-resistance, again, to motions going on in air, is of the same nature as water-resistance to motions going on in water, only less in degree : and as advancing science has shown the true nature of our atmosphere, the amount of this resistance is perfectly ascertained. A smooth ball rolled on the grass soon stops if rolled on a green cloth over a smooth plank it goes longer on the bare plank, longer still on a smooth and level sheet of ice, it hardly suffers retardation from friction, and, if the air be moving with it, will reach a distant shore. Two little wind-mill wheels set in motion together with equal velocity, but of which one has the flat sides of the vanes turned to their course, and the other the edges, if moving in the air, will stop at very different times, but if tried in a vessel from which the air has been removed, they will both go much longer, and will then stop exactly together. As it is to facilitate the motion of fishes in the water, that they are of sharp form before and behind ; so it is to facilitate the motion of birds in the air that they have somewhat of a similar form. A large spinning-top, with a fine hard point, set in motion in a vacuum, and on a hard, smooth surface, will continue turning for hours. A pendulum moving in a vacuum has only to overcome slight friction at its point of suspension, and, therefore, if once put in motion, will vibrate for a day or more. But it is in the celestial spaces that we see motions completely freed from the obstacles of air and friction and there they seem eternal. Had the human eye, unassisted, been able to descry the four beautiful moons of Jupiter, wheeling around him for these thousands of years, with such unabated regularity, and which now form, to the telescope of the astro- nomer, a perfect and magnificent time-piece in the sky, or had science long proved that the velocity imparted to our globe, when first launched into its present orbit, still wheels it along as swiftly as in the days of the first man, this error or prejudice, that motion is always tending to rest, would never have arisen. Indeed, had these or other such truths, been long familiar to the common MOTION UNIFORM. 47 mind, the opposite prejudice might as well have obtained, that motion is the natural state, and rest a forced or unknown state. We know of nothing which is absolutely at rest. The earth is whirling round its axis and round the sun ; the sun is moving round its axis and round the centre of gravity of the solar system, and possibly, round some more remote centre in the great universe, carrying all its planets and comets about his path. If there were any natural tendency in moving bodies to stop, a thing float- ing in a trough of water, on board a sailing ship, should always be found at the end of the trough nearest the stern ; and in all the seas and lakes of the earth, the floating things should be accumulated on the western shores, because the surface of the earth is always turning towards the east. We know that neither of these suppositions is truth. A man on board a mov- ing ship can throw any body just as far towards the bow as towards the stern ; although in the two cases the velocity, as regards the earth is so different. Ignorance of the law of moral inertia led a story-telling sailor to assert, as a proof of the speed of his favourite ship, that when a man one day fell from the mast-head, the ship had passed from under him before he reached the deck : the fact in such a case, being, that he must have fallen on the same part of the deck, whether the ship were in motion or at rest, because his body had just the motion or rest which belonged to the ship. Another equally sapient man, reflecting that the earth turned round once in twenty-four hours, proposed rising in a balloon, and waiting aloft, until the country which he desired to reach should be passing under him. "Motion naturally uniform" (See the Analysis.) It is only repeating that a body can neither acquire motion nor lose motion without a cause, to say that free motion must be uniform. The perfect uniformity of undisturbed motion is proved by every fact observed in the universe. If any continued motion, as of a planet, for in- stance, be found at one time to have certain relative velocity to some other continued motion, the same relation is found always to hold : or deviations from perfect uniformity are exactly proportioned to the disturbing causes. Thus we can foretell the exact time of an eclipse, a thousand years before its occurrence. Had motion not been in its nature uniform, a man could have formed no rational conjecture or anticipation as to future events; for it is by assuming, for instance, that the earth will continue to turn uniformly on its axis, that he speaks of to-morrow and of next week, &c., and that he makes all his arrangements for future emergencies : and were the coming day, or season, or year, to arrive sooner or later than such anticipation, it would throw such confusion in all his affairs, that the world would soon be desolate. To calculate futurities, then, or to speak of past events, is merely to take some great uniform motion as a standard with which to compare all others ; and then to say of the remote event, that it coincided or will coincide with some described state of the standard motion. The most obvious and best standards are the whirling of the earth about its axis, and its great revolution round the sun. The first is rendered very sensible to man by his alternately seeing and not seeing the sun, and it is called a day ; the second is marked by the succession of the seasons, and it is called a year. The earth turns upon its axes nearly 365 times while it is performing one circuit round the sun, and thus divides the year into so many smaller parts, and the day is 48 MOTIONS AND FORCES. divided into smaller parts, by the progress of the earth's whirling being so distinctly marked, in the constantly varying direction of the sun, as viewed from any given spot on the face of the earth. When advancing civilization made it of importance for men to be able to ascertain with precision the very instant of the earth's revolution, connected with any event, various con- trivances were introduced for the purpose ; as, sun-dials, where the shadow travels progressively round the divided circle ; the uniform flux of water through a prepared opening the flux of sand in the common hour-glass, &c. But the great triumphs of modern ingenuity are those astronomical clocks and watches, in which the counted equal vibrations of the pendulum, or balance-wheel, have detected periodical inequalities even in the motion of the earth itself, and have directed attention to unsuspected disturbing causes, important to be known. It is the natural uniformity of undisturbed motion which causes any num- ber of bodies moving together, as the furniture of a sailing ship, to appear among themselves as if at rest, no one tending to pass before, or to fall behind, or to move to one side or another. For the same reason a person who is moving with such bodies is absolutely insensible of his uniform pro- gression, and knows it only by reasoning from such facts as the changing appearance of other objects around which do not share the motion, the rush- ing of the waves or wind, &c. When a ship is becalmed at sea, she may, as numberless sad accidents have proved, be carried by rapid currents in any direction, without one of the crew suspecting that she has motion at all ; and if the suspicion do arise, the truth can be come at only by such means as the sounding line, where the bottom can be reached, or careful observation of the heavenly bodies where it cannot. A man in the hold of a ship in a river or tides-way cannot say whether the rushing of water, which he hears from without, be a rapid tide passing the ship at anchor, or the effect of the ship's advance in the river. A man in a balloon going 80 miles an hour, knows not in what direction he is moving, nor indeed that he is moving at all, but by observing the objects below. This explains why men are not sensible of the motion of the earth itself, which they know, however, to be turning around its axis once in twenty -four hours, and therefore to have its surface near the equator moving with a speed of more than 1,000 feet per second ; and as in the case of a ship or balloon, there will be no difference of sensation whether the speed were of one mile per hour or of 10 or 100, so in the case of the earth, there would be none whether it turned as now, once in twenty-four hours ; or, like the planet Jupiter, once in ten. A hunter among the hills, who during the heat of noon, rests and contemplates around him a sublime scfene of solitude and silence, may little think that if, amidst that apparent repose of nature, he were for a moment lifted up from the earth and held at rest above its sur- face, he would see its face of hill and dale sweeping past beneath him at the prodigious rate of 1,000 miles an hour, on account solely of the whirling of the earth. The fact that a cannon-ball can be shot just as far upon the surface of the earth, eastward, in the direction of the earth's motion, as westward, against it, illustrates the truth, that whatever common motion objects may have, it does not interfere with the effect of a force producing any new relative motion among them. All the motions seen on earth are really only slight differences among the common motions : as in a fleet of sailing ships, the apparent changes of place among them are in reality only slight alterations of speed or direction, in their individual courses. MOTION STRAIGHT. 49 A man continuing to throw upwards a ball or orange, or several of them at once, and to catch and return them alternately, uses no difference of art as regards them, whether he be standing on the earth and whirling with it, or on a sailing ship's deck, or in a moving carriage, or on a galloping horse's back. He and the oranges have always the same forward common motion. And when a man, standing on a galloping horse, leaps through a hoop held across his course, he does not leap forward for this would throw him over the horse's ears but merely jumps up and allows his moral inertia to carry him through. The reason why a lofty spire or obelisk stands more securely on the earth, than even a short pillar stands on the bottom of a moving wagon, is, not that the earth is more at rest than the wagon, but that its motion is uniform. Were the present rotation of our globe to be arrested but for a moment, imperial London, with its thousand spires and turrets, would, by the moral inertia, be swept from its valley towards the eastern ocean, just as loose snow is swept away by a gust of wind. " Force is required to bend motion" If a body moving freely cannot vary its velocity without a cause, neither can it vary its course without a cause ; and free motion, therefore, is straight as well as uniform. A ball shot directly up or down gives men their simplest idea of straight motion. A bullet or arrow, projected horizontally, is gradually drawn downwards by the attraction of the earth, but it deviates neither to the right nor to the left. William Tell, trusting to the natural straightness of motion, obeyed the tyrant's order, and shot an apple placed on his child's head. And the right eye of Philip of Macedon is said to have been destroyed by an arrow which* brought a label on it, telling its destination. Riflemen shooting at a target, hit the very spot they choose to aim at. A stone in a sling, the moment it is set at liberty, darts off as straightly as an arrow from the bow-string or a bullet from a gun-barrel, and it is only because the point of its circle, from which it should depart, cannot in prac- tice be accurately determined, that the same sure aim cannot be taken with it. A body moving in a circle, then, or curve, is constrained to do what is contrary to its inertia. A person on first approaching this subject, might suppose that a body, which for a time has been constrained to move in a circle, should naturally continue to do so when set at liberty. But on reflecting that a circle is as if made up of an infinite number of little straight lines, and that the body moving in it has its motion bent at' every step of the progress, the reason is seen why constant force becomes necessary to keep it there, and force just equal to the inertia with which the body tends, at every point of the circle, rather to Fig. 2. pursue the straight line, called a tangent, of which that point, as seen in Fig. 2, is the commencement, than the circle itself. The force required to keep the body in the bent course, is called centripetal or centre-seeking force ; while the inertia of the body tending outwards, that is, to move in a straight line rather then in a curve, is called the centrifugal or centre-flying force ; and the term cen- tral forces is applied to both. 50 MOTIONS AND FORCES. A sling-cord is always tight while the cord is whirling :,and its tension is of course the measure both of the centripetal and centrifugal force. A means, then, of measuring the tension of a sling-cord would experimentally demon- strate the amount of centrifugal force ; and such a means we possess in the contrivance called the " whirling table/' upon which is a leading sling, or any mass with a string attached to it, may be placed to revolve, at any desired distance from the centre, and with any desired velocity, while the string passing over a pulley at the centre, is made to lift weights proportioned to the outward dragging of the revolving mass. By this apparatus it is found, as would be expected, that centrifugal force in other words the force with which the inertia of moving matter resists the bending of its course from straight to circular, is proportioned, first, to the quantity of matter moved- every separate particle having its own inertia ; second, to the size of the circle or orbit described in the same time a body moving in a circle of double diameter for instance, having to be forced inwards from the tangent, at every departure, twice as far in a given time ; third, that with a double revolution in the same time, the centrifugal force is not double but quadruple (a corresponding proportion existing for other velocities,) because, not only are there twice as many bindings or angular departures from the tangent for the two circles as for one, requiring, as may be said, twice as many tugs or impulses of the centripetal force, but every impulse must be made with double energy, for it has to drive the mass inwards through the required dis- tance in half the time ; and twice as many impulses, every one. being twice as strong, make a quadruple amount of force on the whole ; fourthly and lastly, it is found, agreeing with the relation between inertia and terrestrial gravity described at page 43, that a body revolving, for instance, in a circle of four feet diameter, that it may have centrifugal force just equal to its weight, required to complete its revolution in one second and a half of time. This and similar facts will be more particularly considered when we come to treat of the motions of the planets round the sun. This analysis of central forces will suffice to excite in the student a due interest touching the kindred phenomena now to be described. Bodies laid on a whirling horizontal wheel, are readily thrown off. In a corn-mill, the grain, after being admitted between the stones through an opening in the centre of the upper stone, is then kept turning round between them, and is, by its centrifugal force, always tending and travelling outwards until it escapes as flour from the circumference. A man, if he lie down on a turning millstone with his head near the edge, falls asleep, or dies of apoplexy, from the new pressure of blood on the brain. A wet mop, or bottle-brush, made to turn quickly on its handle as an axis, throws the water off in all directions, and soon dries itself. Sheep, in wet weather, thus discharge the water from their fleeces, by a semi-rotatory shake of the skin. Water-dogs, on coming to land, dry them- selves by the same action. A tumbler of water placed in a sling, may be made to vibrate like a pen- dulum with gradually increasing oscillation, and at last to describe the whole circle, and continue revolving about the hand, without spilling a drop : the water, by its inertia of straightness, or centrifugal force, tending more away from the centre of motion towards the bottom of the tumbler, even when that is uppermost, than towards the earth by gravity. As solid bodies laid on a whirling table are thrown off, so water in a ves- sel caused to spin round in any way, as on the centre of a horizontal wheel, CENTRIFUGAL FORCE. 51 instead of lying at the bottom, is raised up all round, against the sides of the vessel. "Water, poured obliquely into a funnel, runs round the interior of it, and often leaves an open passage of air all the way down through it, as if there were merely a lining of water to the funnel. The centrifugal force of the turning water is a chief reason of this phenomenon : another reason will be considered farther on, under the head of atmospheric pressure. Great whirlpools at sea, and smaller ones, or eddies in rivers, occur when- ever a current is obliged suddenly to bend, as in rounding a point of land or a rock, or in meeting and mingling with a contrary current. The water, by tending to continue its straight motion, falls in behind the obstruction, re- luctantly as it were, and leaves there a pit surrounded by a liquid revolving ridge. Charybdis, in the Mediterranean, and the great whirlpool off the Norwegian coast, are noted examples. It is owing to the centrifugal force in any bending part of a stream of water, that is to say, the tendency away from the centre of the curvature, that when a bend has once commenced, it increases, and is soon followed by others, until that completeflserpentine winding is produced, which charac- terizes most rivers in their course across extended plains. The water being thrown by any cause to the left side, for instance, wears that into a curve or elbow, and, by its centrifugal force, acts constantly on the outside of the bend, until rock or higher laud resists the gradual progress; from this limit being thrown back again, it wears a similar bend to the right hand, and after that, another to the left, and so on. Carriages are often overturned in quickly rounding corners. The inertia carries the body of the vehicle in the former direction, while the wheels are suddenly pulled round by the horses into a new one. A loaded stage-coach running south, and turning suddenly to the east or west, strews its passen- gers on the south side of the road. Where a sharp turning in a carriage-road is unavoidable, the road towards the outside of the bend should always be made higher than at the inside, to prevent such accidents. A man or a horse turning a corner at speed, leans much inward, or to- wards the corner, to counteract the centrifugal force, that would throw him away from it. In skating with great velocity, this leaning inwards at the turnings be- comes very remarkable, and gives occasion to the fine variety of attitudes displayed by the expert ; and if a skater, in running, finds his body inclined to one side and in danger of falling, he merely makes his skate describe a slight curve towards that side, when the tendency of his body to move fttraightly, or its centrifugal force, refusing to follow in the curve, allows the foot to push itself again under the body, and to restore the perpendicularity. Skating becomes to the intelligent man an intellectual as well as a sensitive or bodily treat, from its exemplifying so pleasingly the law of motion. The last example explains, also, why a hoop rolled along the ground goes so long without falling : if it incline to one side, threatening to fall, by that very circumstance, the part touching the ground is made to bend its course to that side, and as in the case of the skater who turns his foot, the sup- porting base is again forced directly under the mass of the body. A coin dropped on the table or floor often exhibits the same phenomenon. It is said to run and hide itself in the corner. Just before falling, if not obstructed, it describes several turns of a decreasing spiral, the minute ex- amination of which is a pleasing mathematical exercise. The reason also why a spinning top stands, will*;be understood here. 52 MOTIONS AND FORCES. While the top is quite upright, the extremity of its peg, being directly under its centre, supports it steadily, and although turning so rapidly, and with much friction, has no tendency to move from the place : but if the top in- cline at all, the edge or side of the peg, instead of its very point, is in con- tact with the floor, and the peg then becoming as a turning little roller, advances quickly, and describes a curve somewhat as a skater's foot does, until it come directly under the body of the top as before. It thus appears that the very fact of the top inclining, causes the point to shift its place, and to continue moving until it comes again directly under the centre of the top. It is remarkable that even in philosophical treatises of authority the standing of a top is still vaguely attributed to centrifugal force. And some persons believe that a top spinning in a weighing scale, would be found lighter than when at rest; and others most erroneously hold that the centri- fugal force of the whirling, which of course acts directly away from the axis, and quite equally in all directions, yet becomes, when the top inclines, greater upwards than downwards, so as to counteract the gravity of the top. The way in which centrifugal force really helps to maintain the spinning of atop is, that when the body inclines.or begins to fall in one direc- tion, its motion in that direction continues until the point describing its curve, like the foot of a skater, has forced itself under the body, again. By reason of centrifugal force also, it is easier to do feats of horsemanship in a small ring as at our theatres, than if the animal were running on a straight road. We see the man and the horse always inclining inwards to counteract centrifugal force, and if the rider tend to fall inwards, he -has merely to quicken the pace ; if to fall outwards, he has to slacken it, and all is right again. If a pair of common fire-tongs, suspended by a cord from the top, be made to turn by the twisting or untwisting of the cord, the legs will separate from each other with force dependent on the speed of rotation, and will again collapse when the turning ceases. Mr. Watt adapted this fact most ingeniously to the regulation of the speed of his steam-engine. His steam- gouernor may in truth be described as a pair of tongs with heavy balls at the ends, to make their opening more energetic, attached to some turning part of the machine. If the engine move with more than the assigned speed the balls open or fly asunder beyond their middle station, and by a simple contrivance are then made to act on a valve which contracts the steam tube ; on the contrary, with too slow a motion, they collapse and open the valve. A half- formed vessel of soft clay, placed in the centre of the potter's table, which is made to whirl and is called his wheel, opens out or widens merely by the force of its sides and thus assists the worker in giving its form. A ball of soft clay, with a spindle fixed through its centre, if made to turn quickly, soon ceases to be a perfect ball. It bulges out in the middle, where the centrifugal force is great, and becomes flattened towards the ends, or where the spindle issues. This change of form is exactly what has happened to the ball of our earth. It has bulged out seventeen miles at the equator, in consequence of its daily rotation, and is flattened at the poles in a corresponding degree. A mass of lead that weighs one thousand pounds at our pole, weighs about five pounds less at the equator, by reason of the centrifugal force. In the planets Jupiter and Saturn, of which the rotation is much quicker than of our earth, the middle or equator bulges out still more even so as to offend an eye which expects a perfect sphere. QUANTITY OF MOTION. 53 If the rotation of our earth were seventeen times faster than it is, the bodies or matter at the equator would have centrifugal force equal to their gravity, and a little more velocity would cause them to fly off altogether, or to rise and form a ring around the earth like that which surrounds Saturn. Saturn's double ring seems to have been formed in this way, and is now supported chjefly by the centrifugal force of the parts. Were it to crumble to pieces, the pieces might still revolve, as so many little satellites. His true satellites are only more distant masses sustained in the same manner. And our earth and the other primary planets have the same relation to the sun that these satellites have to Saturn all being sustained by an admira- ble balance between centrifugal force and gravity. " The quantity of Motion in a body measured by the velocity and quantity of matter. If a single atom of matter were moving at the rate of one foot per second it would have a definite quantity of motion expressed by these words ; and if it were moving ten feet per second, it would have ten times the quantity. Again, in a mass consisting of many atoms, the quantity of motion would be still as much greater as there were more atoms in it than one. By experiment it is found, that if a ball of soft clay of one pound, sus- pended by a cord as a pendulum, be allowed to fall with a velocity of ten feet per second, against u ball of nine pounds suspended in the same way, but at rest, the two, after contact, will start together at the rate of one foot per second, the original quantity of motion being then diffused through ten times the quantity of matter, and therefore exhibiting only one tenth of the velocity. A cannon ball of a thousand ounces, moving one foot per second, has thus the same quantity of motion in it as a musket-ball of one ounce, leaving the gun-barrel with a velocity of a thousand feet in the second. " The quantity of motion in a body is the measure of the force which pro- duced it." The experiment of the balls of clay mentioned above furnishes one instance of this truth. Again, a body falling for ten seconds, acquires ten times as much velocity as by falling for one second ; its motion thus measuring the force of gravity which has been exerted upon it. When a large body or mass of many atoms falls, it of course has as much more motion than a smaller body, as there are more atoms in it than in the smaller ; but as gravity acts equally on every atom, the force causing either body to fall is still exactly indicated by the quantity of motion in it. A large body or mass of many atoms falls where there is no impediment, with the same velocity as a smaller body or a single atom ; for gravity pulls equally at each atom, and must overcome its inertia equally, whether it be alone or with others. This remark contradicts the popular opinion, that a large and heavy body should fall to the earth much faster than a small and light one ; an opinion which has arisen from our constantly seeing such contrasts, as the rapid fall of a gold coin, and the slow descent of a feather. The true cause of the contrast is, that the atoms of the feather are much spread out, so as to be more resisted by the air than those of the gold. If the two be let fall toge- ther in a vessel from which the air has been extracted as in the common air-pump experiment, they arrive at the bottom in exactly the same time; 54 MOTIONS AND FORCES. and even in the air, if the coin be hammered out into gold leaf, it will fall still more slowly than the feather. One brick dropped from a height, be- cause its motion is not much affected by the air, reaches the earth very nearly as soon as ten bricks let fall near it, whether they be connected or separate as a single horse may reach the goal as soon as ten horses gallop- ing abreast. A man's force will move a small skiff quickly, a loaded barge very slowly, and a large ship in a degree scarcely to be perceived. In each case, however, the quantity of motion may be the same, and a true measure of the force which produced it. A ball of one pound weight, impelled by a given force, moves twice as fast as a ball of two Bounds impelled with the same; yet, although the velocities are different, the quantities of motion, as ascertained by the rule already given, are equal, and indicate an equality of producing force. " The quantity of motion in a body is the measure also of the force or mo- mentum which it can exhibit again" (See the Analysis, 42. ) Bodies, owing to their inertia, may be regarded as passive- reservoirs of force or motion, always ready to return as much as they have received. Mo- mentum is the name given to the motion in a body; with reference to the production by it of new motions or the overcoming of resistances, and is but another term for the quantity of motion A cannon ball, according to the quantity of motion in it, may have only the force or momentum that will bruise a plank, or it may have enough to penetrate a tree, or even to shoot its rapid way through a block of the hardest stone. A block of wood floating against a man's leg with moderate velocity, would be little felt; but a loaded barge, coming at the same rate and press- ing it against the quay, might break the bones; a large ship, again, although moving no faster, would crush his body against any fixed obstacle ; and an island of ice, opposed in its approach to another, even by a first-rate man-of- war, would destroy it, as meeting barges destroy a floating egg-shell. A hail-stone falling, strikes rudely ; a stone rolled from a height, as of old, by the besieged against besiegers, may carry death with it to many ; an avalanche, breaking from its hold on a mountain steep, may sweep away a village. To meeting bodies, the shock is the same, whether the motion be shared be- tween them or be all in one. If a running man come against a man who is standing, both receive a cer- tain shock. If both be running at the same rate in opposite directions, the shock is doubled. In some such cases, as where swift skaters have met, the shock has proved fatal. The meeting fists of boxers not unfrequently dislocate or break bones. A man's skull is fractured as certainly by its being dashed against a tree or beam, while he is on a galloping horse, as by a blow of a similar beam coming upon him with the velocity of the horse. When two ships in opposite courses meet at sea, although each may be sailing at a moderate rate, the destruction is often as complete to both as if with a double velocity they had struck on a rock. Many melancholy in- stances of this kind are on record. In the darkness of night a large ship has met one smaller and weaker, and in the lapse of a few seconds, have followed DIRECTION OF FORCES. 55 the shock of the encounter, the scream of the surprised victims, and the hor- ribly silence when the waves had again closed over them and their vessel for ever. In November, 1825, on the coast of Scotland, the Comet steamboat was thus destroyed, and carried to the bottom with her about seventy pas- sengers, into whose ears the drowning water rushed before the sound of ar- rested music and joy had died away, " Direction of the force or forces producing motion." When only one force acts on a body, the body obeys in the exact direction of the force. A ball floating in water, or lying on smooth ice, is driven exactly south by a wind blowing to the south. A bullet issues from the mouth of a cannon, in the direction of the axis of the cannon which is, as the force impels it. "When two or more forces, not in the same direction, act upon a body at the same time, as it cannot move two ways at once, it holds a middle course between the directions. This course is called the resulting direction, viz., resulting from the composition of the forces. A ball or ship moving south by a direct wind, may, at the same time, be carried east, just as fast, by a tide or current moving east ; every instant, therefore, it will go a little south and a little east, and really will describe a middle line pointing south- east. These particulars may be well represented on paper, as by fig. 3 : where b is the original place of the ball or ship, e the east, s the south, and b a the middle line pointing to the south-east, and showing the true ceurse of the vessel. This figure is called the parallelogram of forces, and is an important help to the understanding of many facts in natural philosophy. The minute investigation of the subject belongs to the science of measures, or technical mathematics ; but the general truths are quite intelligble to common sense, or the mathematics of common experience. When two forces act upon a body, like the wind and tide in the last example, the result is the same, whether they act together or one after the other. For instance, if the wind drive a vessel one mile south, as from b to s, fig. 3, and immediately afterwards the tide drive it one mile east, as s to a, the vessel will be in the same place at last, viz., at a, as if she had been driven at once south-east, in the line b a, by the simultaneous action of the two. Therefore, by drawing the lines b s and b e to represent the force and direction of the two causes of motion, and by then adding one of them, or an equivalent, to the end of the other as s a to b s, or e a to b e, the square or parallelogram is sketched, of which the middle line or diagonal, as it is called, shows the resultant of the forces, and the true course of the body obeying them. What is thus true of the effect of continued forces like wind and tide is Fig. 3. Fig. 4. Fig. 5. Fig. 6. Fig. 7. 56 " MOTION SAND FORCES. true also of momentary impulses, like the blows of clubs simultaneously striking a ball, or of two billiard-balls striking a third. When the forces exactly cross each other, and are equal, as in the case of the ship above supposed, the figure becomes a square, at fljg. 3 ; but if one of the forces be greater than the other, the figure becomes oblong, as at fig. 4 ; if the forces cross obliquely, the fig. becomes as at fig. 5 ; and if they cross in an opposing direction, it will be as at fig. 6. In all the cases, however, the diagonal still shows the result. It is evident that the same line may be the diagonal of many figures, as seen in b a at fig. 7 } and therefore, that very different degrees and directions of combined forces may produce the same result. Forces crossing each other so obliquely as to be represented by lines drawn in almost opposite directions, would form a parallelogram having scarcely any breath, that is to say, the diagonal would approach to nothing; showing thus, that opposing forces neutralize or destroy each other. In fig. 6, by reason of this crossing, the resultant is less than either of the constituents. And for the same reason, when forces cross so acutely as to advance nearly parallel to each other, the resultant is longer than either, as seen in fig. 5. Forces directly opposed, or entirely agreeing in direction, give as their re- sultant their difference or their sum. Forces crossing each other directly, or at right angles, as is true of the exactly eastward force b e, and the exactly southward force b s, in figures 3 and 4, do not in the slightest degree neutralize or alter each other, for the body, when arrived at a, is just as far east as it would be at e, and as far south as it would be at s. This explains why the progressive motion of the planets in their orbits is not at all affected by the directly crossing centri- petal force of gravity which keeps them at their due ( distances from the sun. In all cases where the two crossing forces are equal, with whatever ob- liquity they cross, the resulting direction must be midway between them. Thus a boat impelled by oars, goes straight, although the direction in which the oar acts is constantly changing ; because the changing obliquity of the force is always the same on both sides. This explains also why a bird fly- ing, or a man swimming, holds a perfectly straight course, although in both cases the direction of the impelling forces is constantly varying. And it explains why a body suspended, as a plummet, or falling to the earth as an apple does from a tree, is always in a line towards the centre of the earth : for, while the part of the earth immediately under the body is pulling it straight down to the centre, the action of parts on any one side of the perpendicular is exactly counterbalanced by the action of corresponding parts on the opposite side ; and the perpendicular is still the diagonal or middle line of every pair of attracting parts. In fig. 8, b a represents the common diagonal. In speaking of the attraction of our earth, there- fore, which really is the united attraction of all the individual atoms, we may always consider it as a single force acting to- wards the centre of the earth. When a body is carried below the surface of the earth, its weight becomes less, because the matter then above it is drawing it up, instead of down, as before. A descent of a few hundred feet makes a sensible difference, and at the centre of the earth, if man could reach it, he would find things to have no weight at all ; and there would be neither up nor down, because bodies would be attracted equally in all directions. When more than two forces act on a body, the resulting direction may be DIRECTION OF FORCES. 57 found, first of two, and then of the last resultant with each of the others successively : or the forces may be represented on paper by lines tacked together, of which one denotes the strength and direction of each : the ex- tremity of the last line will mark the place of the body after being acted upon by the combined forces. A sailor, to know the true place of his ship and the course which she has steered, considers, first, the forward progress as found by the log, then the leeway or sideward motion produced by a cross wind, and then the effect of any tide or current in which he may be sailing. Resolution of Forces is a phrase pointing to another important use of such parallelograms or figures as have just been described, viz., the enabling us when force or motion is given, to find the forces or motions in any other directions of which it may be the resultant, and those into which it may itself be resolved. Thus, if a line b a (in any of the preceding figures 4, 5, 6, &c.) represent a force or motion, and the line b s represent one of two elements composing it, we have but to complete the parallelogram b s a e to obtain the other line, b e representing the only other force or motion which, combined with the first element, can produce the given resultant. If a ship pass from b to a (fig. 5) while sailing through the water eastward, a distance expressed by b e, she must at the same time have been carried by a tide current to the distance and in the direction marked by the line b s. Again, if a line be given representing a single force or motion as b a, and if it be desired to know Fig. 9. how much there is in this capable of acting in another jy e direction as b d ; it is only necessary to draw a line f\ - C in the direction, as b d, from the commencement of b a, and to cut such line by another drawn directly upon it or at right angles to it, as the term is, from the other end of b a : the length of b d, so cut off, viz., b s, shows the proportion required. It is thus that a sailor who knows how far he has sailed in an oblique direction finds out how much he has gone north and east or south and west j in other words, finds out the difference in latitude and longitude between his present place and a former one. In the above figure, b a may represent the course and distance sailed, b s the difference of latitude, and b e the differ- ence of longitude. Thus again, if a ball b strike a table a c, with velocity and direction, both represented Fig 10. by the line be; and if the ball be supposed afterwards with the same velocity to approach the table in the oblique directign e c, it will then strike with as much less force than before, as the line e a is shorter than e c. For e a is found according to the rule for decomposing a force, given above; and, to common sense, it is obvious, that if the whole velocity of the ball be represented by e c, the rate of approxi- mation towards the table, or merely downward . velocity and therefore the downward force is marked by the line e a. The body only falls through the distance e a while moving all the way from e to c. O 58 MOTIONS AND FORCES. Figure 10, explains the important cases of the force of wind upon ships sails, windmill vanes, &c. ; and the force of water upon float-boards, water- wheels, &c. ; showing that the moving mass exerts force upon a surface, not in proportion to the speed with which it may he passing along or near the surface, but to the rate of perpendicular approximation. It explains also, why the slanting blow of a club or ball is so light, compared with the direct blow. " The two great forces of Nature ore Attraction and Repulsion." (Read the Analysis.) A person, on first approaching this subject, is far from supposing that the beautiful and almost endless variety of phenomena exhibited in the universe around, all are referrable to the two principles, attraction and repulsion^ examined in the first section : but such is the truth. It will first be shown here, how the great classes of accelerated, retarded, and bent motions arise from them. Attraction. Until Newton said, that what we call weight of bodies is merely an instance of that universal attraction of matter which diminishes with increasing distance, it was never suspected that weight was less, high up in the air than on the ground ; or on a lofty mountain than on the sea- shore. But this we now know to be the case. However, in studying what goes on in obedience to gravity near the surface of the earth, except in a few very nice cases, gravity may be considered as a uniform power ; for man has neither approached the centre of the earth in mines, nor receded from it in balloons, by more than about a thousandth part of his distance from it; and weight has relation to the distance from the centre, not to the distance from the surface. 11 Accelerated Motion from Gravity" Owing to the inertia of matter, any force continuing to act on a mass which is free to obey it, produces in the mass a quickening or accelerated motion ; for as the motion given in the first instance, continues afterwards without any farther force, merely on account of the inertia, it follows, that as much more motion is added during the second instant, and as much again during the third, and so on. A falling body, therefore, under the influence of attraction, is, as it were, a reservoir, receiving every instant fresh velocity and momentum. It is said that Newton's sublime genius read the nature of attraction in the simple incident of an apple falling before him from a lofty branch in his garden. The eye which perceives an apple beginning to fall, can follow it for a time and mark the gradual acceleration of its descent, but soon sees its path only as a shadowy line. A boy letting a ball drop from his hand, can catch it again in the first instant, but after a litttle delay his hand pursues it in vain. A fragment of rock, detached from thejwow of a hill by the lightning stroke, begins its motion slowly; but once fairly launched, it gathers fresh speed and*momentuni with every instant, and bounds from steep to steep driving every obstacle before it. Any liquid falling from a reservoir, forms a descending mass or stream, of which the bulk diminishes from above downwards, in the same proportion as the velocity of the particles increases. This truth is well exemplified in the pouring out of molasses or thick syrup; if the height of the fall be con- siderable, the bulky sluggish mass, wliich first escapes, is reduced, before it reaches the bottom, to a small thread; but the thread is moving proportion- ately faster, and fills the receiving vessel with surprising rapidity. The same MEASURE OF ATTRACTION. 59 truth is exhibited on a vast scale in the falls of Niagara; where the broad river is seen first bending over the precipice a deep slow moving mass, then becoming a thinner and a thinner sheet as it descends, until at last, sur- rounded by its foam or mist, it flashes into the deep below, apparently with the velocity of lightning. When velocity becomes considerable in any case of falling; it cannot be measured accurately by thereye, but its effects ascertain it. A man leaps from a chair with impunity, from a table with a shock, from a high window with fracture of his bones, and in falling from a balloon his body is literally dashed to pieces. The force of gravity or general attraction is such at the surface of this earth, that, in the first second of time, it gives to a body allowed to fall a velocity of 32 feet nearly per second, that is, a velocity which, remaining uniform from the end of the second, would carry it, without farther action of gravity, through 32 feet in the next second Yet the body falls only 16 feet in the first second; and the reason is, that the velocity of 32 feet pos- sessed at the end of the second is gradually acquired, the body having only half of it at the half second, and as much less than half at any distance be- fore that time, as it has more than half at the same distance afterwards; and the average, therefore, is only half of the 32, or 16 feet in the whole second. In the next second, it falls, of course, through the whole 32 feet, with 16 additional, from the new action of gravity, in all three times as much as in the first second; and in two seconds, therefore, it falls altogether four times as far as in one second. At the end of two seconds the velocity is doubled or is 64 feet per second, so that in the third second the body falls 64, and other new 16, in all five times as much as in the first second ; and in three seconds, therefore, it has descended nine times as far as in one second, &c. Knowing this progress, the velocity acquired by a falling body, and the dis- tance through which it falls, in any given time, are easily calculated ; and the height of a precipice, or the depth of a well, may be ascertained by marking the time required for a body to fall through the space. The doctrines of falling bodies are of such importance in the minute ex- amination of many of the phenomena of nature, that much attention has been bestowed upon them. Mr. Atwood's ingenious contrivance by which the motion of falling bodies may be retarded in any desired degree, without the character of the motion being otherwise altered, has enabled experimenters to render evident to the senses all that abstract calculation had anticipated. A pound weight, left quite free, falls towards the ground, sixteen feet in the first second, proving that attraction of one pound is just sufficient to over- come the inertia of one pound at that rate. But if the inertia were doubled, or tripled, or increased in any other degree, the fall of course would be just so much slower. Now Mr. Atwood's machine in effect increases it, by causing falling weights to overcome not only their own Fig. 11. inertia, but also that of other weights; fig. 11. Thus a and b, being weights of two pounds each, balancing each other over the very easily turned pulley c, are moved by a weight of one pound d, hooked to one of them ; and gravity in pulling this down, with force of one pound, has to overcome, not the inertia of one nound, but of five, for the other two weights must move as fast as the one pound does ; and thus, the velocity being reduced to one-fifth of what is natural to a falling body, the d~* he follow- ing equation, which expresses all the circumstances of uniform motion. Let t the time of motion, * = the space described in the time j?, v = the velocity; Then, s = v t from which we obtain * v = t s and t = APPENDIX. 77 Of Gravity. Prop. 28. The force which causes bodies to fall to the earth is of the kind named constant, and is called gravity, p. 58. Prop. 29. The direction of gravity is in lines perpendicular to the earth's surface. Prop. 30. The force of gravity is directly proportional to the mass of the body. For however small the parts into which we divide a body, we find them all affected by gravity, since this force must act upon all the particles of a body. Hence, in an unresisting medium, all bodies setting out from a state of rest, fall through the same space in the same time, because the force of gravity acting upon them increases in proportion to the mass to be moved. Prop. 31. The force of gravity decreases, as the square of the distance from the attracting body increases. This is proved by astronomical observations. Motion produced by joint forces. Prop. 32. When a body is acted upon at the same moment by a plurality of forces, each of these forces produces its full effect : and the place of the body at the end of any given time is the same as it would have been if the forces had acted in succession each during that time, pp. 55, 56, 57. Thus let A B represent the direction of a force that would move a body, A the distance from A to B in a certain interval of time, (a second for example,) and A 0, the direction of a force that would propel the same body from A to C in the same interval of time. Suppose the first force acted alone, it would move the body from A to B in one second ; if the force A C then acted at B, by drawing B R equal and parallel to A C, B R will represent the direction and velocity of the force A C, and R the position in which the body would be in at the end of the second interval of time. Unite A and R and the line A R will represent the course of the body A if acted upon at the same moment by the two forces A' B and A C, and R the position of the body at the end of the first interval of time. In the same manner the action of anynum- Fig. 19. ber of forces may be represented. Thus let A B, A C, A D, A E, represent the separate effects of four different forces acting in the same plane, capable of moving a body the distances A B, A C, A D, A E, in a given interval of time. Draw B c, c d, d R, equal and parallell to A C, A D, A E, respectively, and join A R, A B, c d R, will represent the path of the body if these forces had acted successively each during one interval of time, and A R the path of the body if they all act together, and R the position of the body at the end of the first interval of time. Prop. 33. The line A R in figures given to illustrate the preceding propositions represents the direction and measure of a single force equivalent to all the others in each figure ; and hence the process by which it is deter- mined called the composition of forces, pp. 55, 56, 57. 78 APPEXDIX. Prop. 34. Any force may be decomposed into any number of other forces, that shall be equivalent to it, by the reverse of the foregoing operation. This process is called the Resolution of forces, p. 57. Thus the force A R, fig. 18, may be separated into two forces A B, A C, and the force A R, fig 19, into four forces, A B, A C, A D, and A E. Prop. 35. When the forces act in the same right line, we have only, in order to ascertain the spaces described by their combined action, to add or substract the spaces which would be described by their separate action, ac- cording as these forces act, in the same or opposite direction. Equilibrium. Prop. 36. A body acted upon by a plurality of forces, in opposite direc- tions, will remain at rest, or in equilibria; when these forces were supposed to act in succession each during the same interval of time, the body would arrive at its point of departure. The simplest and most evident case of equilibrium is that in which a body is acted upon by two equal and opposite forces. On the joint action of an impulsive and a constant force. A. When these forces act in the same manner. Prop. 37. When the forces act in the sam'e direction, the place of the body at the end of any given time, may be determined, as in the problem of the composition of forces, by supposing, first, that the impulsive force acts during that time, and then that the action of the constant force commences and acts alone during the same time : the spaces added altogether will give the space passed over by the joint action of these forces during the assumed time. Prop. 38. When the forces act in opposite directions, the place of the body may be ascertained by a similar process ; in this case, however, the spaces are to be substracted one from the other, pp. 58, 59. When a constant force is acting in a direction contrary to that of a moving body set in motion by an impulsive force, the retardation that the former produces may be determined by comparing the motion wifh that of a body moved by the same force. The degrees by which an ascending body loses its motion, are the same as those by which it is again accelerated at the same points, when it has acquired its greatest height and again descends, for the velocity at the corres- ponding parts of the ascent and descent are equal. Thus we may calculate to what height a body will rise when projected upwards by an impulsive force, gunpowder, for instance, and retarded by the force of gravity. Since the force of gravitation produces or destroys a velocity of 32 feet in every second, a velocity of 320 feet will be destroyed in 10 seconds; and accord- ing to what has been premised, a body will fall in 10 seconds through a hun- dred times 16 feet or 1600 feet, which is therefore the height to which a velocity of 320 feet in a second will carry a ball projected, without resistance from other cause than gravity, 'in a vertical direction, p. 60. B. When these forces act in different directions. * When the successive directions of the constant forces are parallel. Prop. 39. If the constant force be that of gravity, the successive direc- APPENDIX. 79 Fig. 20. tions of which are assumed to be parallel, the investigation of the effects produced constitutes the doctrine of projectiles; a projectile being a body thrown in any direction by an impulsive force and at the same time acted upon by the force of gravity, pp. 59, 60. Prop. 40. The place of a projectile at' the end of any given time may be determined as in the problem of the composition of forces, by supposing first that the impulsive force alone has acted during that time, and then that the action of gravity commences, and acts alone during the same time. Thus let A H represent a hori- zontal plane, and A B the initial direction and velocity of a body projected from the point A in the same plane. If the impul- sive force alone acted on the body it would describe the path ABB' B" B'" &c. with uniform velocity. But as the force of gravity acts from the moment of projection, the body will be drawn downwards from the line A B'" so as to be found after the successive intervals of time, at the points g g' g", &c., and as the force of gravity produces a velocity which increases as the squares of the distances^ if the distances A B, B B', B' B", B" B'" be equal, B g, B' g', B" g", B"' g"', &c., will be as the squares of these dis- tances 7 and the path of the projectile through the points g g' g" g'" will be a curve, and this curve mathematicians have called aparabola. ** When the successive directions of the constant force tend to a common centre. Prop. 41. This case constitutes the doctrine of central forces, see prop. 13, p. 75. Prop. 42. The place of the body at the end of any given time may be determined here also by the problem of the resolution of forces. Thus, suppose A represent a body impelled towards H with such a force, as, by itself, would enable it to run over the equal spaces A B, B F, F G-, &c., in equal portions of time : suppose like- wise that it is acted upon the same time by con- stant force, which would enable it to pass over the unequal spaces A I, I K, K L, &c., in the same equal portions of time. It is evident, that the joint action of both these forces would compel the body A to pass over the curvilinear path A N P, &o. Through B draw the line B C, (viz., in the centre of attraction); through I draw I N par- allel to A B ; and at the end of the first portion of time the body will be found at N, whence it would proceed in the straight direction N R (by the first law of motion), if the constant force then ceased Fig. 21. 80 APPENDIX. to act. But as this force continues to act, the body at the end of the second portion of time will be found in ; for the like reason, at the end of the third portion of time, it will be found in P, and so on. The course then A N P is not straight, but consists of the lines A N, N 0, P, forming certain angles with each other. Now it will not be difficult to conceive that, because the attractive force acts not by intervals but constantly and unremittedly, the real path of the body must be a polygonal course, consisting of an infi- nite number of sides; or more justly speaking, a continuate curved line, which passes through the points A, N, 0, P, &c., as is shown by the dotted line. Prop. 43. Should the action of the centripetal force cease at any instant, the body would proceed straight forward, p. 49. The portion of the impulsive force by which this is affected is called the centrifugal, prop. 14. Prop. 44. Whilst the distance from the centre remains unchanged, as when the body moves in a circular orbit, the centripetal and centrifugal forces are equal. Laws of Central forces. Prop. 45. When bodies revolve in equal circles, their centrifugal forces are proportional to the squares of their velocities. Prop. 46. When two bodies revolve with equal velocities at different distances, the centrifugal forces are inversely as the distances. Consequently (prop 45,46) the centrifugal forces are in all cases directly as the squares of the velocities, and inversely as the distances. Prop. 47. When two bodies revolve in equal times at different distances, their centripetal forces are simply as their distances. In general, the centripetal forces are as the distances directly and as the squares or the times of revolution inversely. Prop. 48. WheR the forces vary inversely as the squares of the distances, as in the case of gravitation, the squares of the times of revolution are pro- portional to the cubes of the distances. Thus, if the distance of one body be four times as great as that of another, the cube of 4 being 64, which is the square of 8, the times of its revolution will be 8 times as great as that of the first body. Prop. 49. Where the orbit deviates more or less from a circular form, a right line joining the revolving body and its centre of attraction, always de- scribes equal areas in equal times, and the velocity of the body is therefore always inversely as the perpendicular drawn from the centre to the tangent ; and the velocity at any point less than three-eighths, greater than that neces- sary to make the body describe a circle. Prop. 50. To propel a body in an elliptical orbit, the force directed to its focus must be inversely as the square of the distance. This is proved by astronomical observations, but we have no other proof of it. The motion of the planets round the sun in the solar system is governed by the laws of central forces, the centripetal force in this case being that of gravity. On the joint effect of active and inactive forces. A. When they have opposite directions. Prop. 51. The effect of passive forces is to restrain and modify the action of other forces so as to confine the motion of a body to a particular course or path, and the direction of the passive force affecting a body at any moment APPENDIX 81 s the line perpendicular to that part of this path at which the body is found at this moment. If the direction of the active force be also perpendicular to this path, the body must evidently remain at rest, since no part of this force can be resolved into the direction of the path in which alone the body can move. B. When they have different directions. General rule. Prop. 52. Resolve the active force into two, one perpendicular, and the other a tangent to the path of the body, the effect of the former force will be entirely destroyed (prop. 51,) and the body will advance by the latter alone, , * On the motion of a body impelled obliquely against a plane. Prop. 53. Let M N represent the plane, Fig. 22 and A B the direction and velocity from the impulsive force, resolve A B into the forces A C perpendicular to the plane, and C B in its direction, then by the general rule (prop. 52) the body will move along the plane witlra velocity of which C B is the measure. K On the motion of a body impelled obliquely against a curved surface. Prop. 54. Let M N represent the curve and Fig. 23. A B the direction and velocity from the impul- sive force. Resolve A B into two forces, C B perpendicular to the curve at B, and B D (equal to A C) a tangent to the curve at the same point. Then B D will represent the velocity at the point B. Prop. 55. If the curve be interrupted at any point, or change the direction of its concavity, the body will advance with its last velocity in a tangent to the curve at that point. *** On the descent of a body along an inclined plane. Prop. 56. Let M N represent an in- clined plane and A B (perpendicular to the horizontal base H NJ the force of gravity as measured by the distance which would cause a body to descend in the first second of time. Resolve A B into two, A C, per- pendicular to the plane, and C B in its direction, then the body will be urged down the plane by the constant force measured by C B. Laws of the descent of bodies down inclined planes. Prop. 57. 1st. The motion of a body drawn down an inclined plane is uniformly accelerated. Prop. 58. 2d. The velocity acquired is proportional to the perpendicular 6 82 APPENDIX.. descent, so that a body falling from M to H has the same velocity at H as one descending the whole length of the plane at N. Prop. 59. 3d. The times of descent down planes of the same heights are as their lengths. Prdp. 60. 4th. The times of descent down all planes which are cords drawn to the lowest point of the same circle, are equal. Thus, if the balls A, B, C, be placed at different Fig- 25 points of the circle and suffered to descend at the same instant along as many planes which meet at the lowest point of the circle, they will arrive there at the same time. Or it may be enunciated in the following terms : the times of descent down all the cords drawn from the same point or circumference of a circle will be the same. This will be made evident by supposing the above figure inverted, D being made the upper point and the balls allowed to fall from that point to A, B, and C.* **** On the descent of a body down a vertical curved line. Prop. 61. The times of descent down the cords of different circles are to each other as the square roots of their diameters. Prop. 62. If a body fall from a state of rest down a curve, the velocity acquired is equal to that which it would have by falling through the same perpendicular height. For if the curve be considered as made up of an infinite number of con- tiguous planes, it is evident that the angle of inclination of any two of these adjacent planes is infinitely small, or nothing, and consequently there is no velocity lost by a change of direction in passing from one to the other. Therefore, as the effect of gravity is not impeded, the truth of the proposi- tion becomes evident. Prop. 63. If a body be projected up a curve, the perpendicular height to which it will rise is equal to that through which it roust fall to acquire the velocity of projection. For the body in its ascent will be retarded in the same degree that it was accelerated in its descent* Thus, let B A B' be a curve in which the lowest Fig. 26. point is A, and the parts A B, A B' are similar ; a body in falling down B A will acquire a velocity that will carry it to B', and since the velocities in all equal altitudes in the ascent and descent are equal, the times of ascent and descent are equal. The foregoing proposition is equally true whether the body actually move over a solid surface or be retained in its path by a string which is in every part perpendicular to it. Of the simple Pendulum. Prop. 64. The simple pendulum is conceived to be a mere material point suspended by an imponderable and inextensible thread, p. 60. Prop. 65. If the simple pendulum vibrates through very small arcs, these may, without sensible error, be conceived to coincide with their chords, and we may derive from this consideration the following theorems : 1st. As the times of descent of the body down different chords of the same APPENDIX. 83 verticle circle are equal (prop. 60.) the vibrations of the same pendulum, although performed through unequal arcs, will be very nearly equal, p. 61. 2d. The times of vibrations of different pendulums will be to each other as the square roots of the lengths of these pendulums, or, which is the same thing, their lengths are proportioned to the squares of the times of vibration, p. 61. The times of descent down the chords of different circles are the same as would be occupied in descending vertically through their diameters, and are consequently proportional to the square roots of these diameters. Of the impact of bodies. Prop. 66. When a body in motion strikes directly another body, it always communicates motion to the second body, and loses part of its own, and from the third law of motion it is evident that the momentum gained by the second body is exactly equal to that lost by the first. Prop. 67. When one non-elastic body strikes against another, the two bodies will move on together since there is no force to separate them ; and as one of the bodies gains all the momentum which the other loses, the momen- tum after impact will be equal to the sum of the momentum before impact. Prop. 68. When an elastic body strikes against another, the second is impelled forward with double the momentum which it would have received under the same circumstances if non-elastic. For at the moment of impact the form of the body struck is changed by a force equivalent to the momentum which it receives from the striking body, and if this body be perfectly elastic, its form will be restored to it by a force exactly equal to that by which it was changed, and this force (which we have just seen to be equal to the original impulse,) will be exerted in driving the body forward. The body thus receives, besides its original impulse, the equal force of the re-bound. Prop. 69. The striking body, when elastic, is also acted upon by the rebound, and loses twice as much momentum as it would have lost if non-elastic. In this case, as in the former, the sum of the momenta is the same after impact as before it ; but the bodies after impact do not move on together. Prop. 70. If an elastic body strike against a firm plane, the angle of reflection will be equal to the angle of incidence, p. 66. 84 MECHANICS. PART II. PHENOMENA OF SOLIDS. THE FOUR FUNDAMENTAL TRUTHS USED TO EXPLAIN THE PECULIARI- TIES OF STATE AND MOTION WHICH DEPEND ON THE SOLID FORM OF BODIES j A DEPARTMENT COMMONLY CALLED MECHANICS. ANALYSIS OF THE CHAPTER.* A force, which moves part of a solid body, must effect the whole or break off the part. If the force be directed towards a certain central point in the mass, it will effect the whole equally, whether simply to support the mass, or to move it or to stop it when in motion. The point, according to circumstance, is called THE CENTRE OF GRAVITY OF INERTIA, OT OF ACTION. In solid bodies moving about an axis, as exemplified in a wheel or weigh- ing beam the various parts describe circles or move through spaces which are greater in proportion to their respective distances from the centre of motion. Hence forces differing as to speed, may still, through a solid medium, be brought exactly to co-operate or to oppose one anotJier j a slow force counter -balancing or being equivalent to a quicker one, provided tliat it be more intense in proportion as it is slower. The SIMPLE MACHINES, or MECHANICAL, MEDIA Called LEVER, WHEEL AND AXLE, PULLEY, INCLINED PLANE, WEDGE, SCREW, &c., are so many arrange- mentsof solid parts, by which forces of different velocities and intensities maybe thus connected or opposed, or may be conveniently substituted one for another . By solid connecting parts, also, the direction of any existing motion or force may be changed, as when the straight motion of running water is con- verted into the rotary motion of a water-wheel, &c. Hence arises an end- less variety of COMPLEX MACHINES. In all machines, an important circumstance to be considered is the resist- ance among moving parts which arises from FRICTION : and in solid structures generally, the forms and positions of parts have to be adjusted to the STRENGTH OF THE MATERIALS, and to the strains which the parts have to bear. " Solid" is the term applied to a mass in which the mutual attraction of the atoms is so strong, that the mass may be moved about as one body, with- out the relative positions of the component parts being thereby disturbed. " Force moving part of a solid must effect the whole or break off the part." This is a necessary consequence of the description or definition of a solid just given. And it follows that in all cases of breaking, the cohesion of the * The reader .should here re-peruse the general table or synopsis at page 19. CENTRE OF GRAVITY. 85 atoms at the fractured part must have been less strong than the weight of the remaining mass, or its inertia resisting the degree of change attempted, or the force fixing it to its place, or than some combination of these particulars. The sharp blow of a hammer given to 'an ivory ball, causes it to dart off swiftly, but does not injure it, because the -cohesion among the atoms struck is stronger than the opposing inertia of the mass, even under a rapid change ; but the blow of a hammer on a large elephant's tusk indents or breaks the part because the opposing inertia of the larger mass is stronger than the cohesion of the atoms which receive the blow. A vessel of pottery- ware may be safely suspended by its handle ; proving that the cohesion which fixes the handle to it is stronger than the weight of the vessel ; but if the attempt be made to lift the vessel quickly, the handle may rise and leave the vessel behind ; because then the weight and inertia are acting together to destroy the cohesion. Thus servants attempting to lift too quickly the loaded stone-ware dishes at a dinner-table, often break off the part by which they take hold. Centre of Gravity or Inertia. If any uniform beam or rod be supported by its middle, like a weighing beam, the two ends will just balance each other. This is in accordance with the general truth or law of attraction already explained; for as there is just as much similarly situated matter on one side of the support as on the other, there will also be just as much attraction, and therefore no reason why the matter on one side should overpower that on the other. If equal weights be afterwards attached in corresponding situations on the two arms of the beam the balance will not be thereby disturbed; and the operation of adding weights that counterpoise, above and below, and near and far from the centre may be continued, until a bulky mass is built up upon the beam and in- stead of a beam a wheel may be used yet the whole will remain perfectly supported and in equilibrium about the original centre. In the pages now to follow, it will be shown that, in every body or mass, or system of con- nected masses, in the universe, there is a point of this kind about which all the parts balance or have equilibrium, and it is this point which is called the centre of gravity or of inertia. Although in any mass, therefore, every atom has its separate gravity and inertia, and the weight and inertia of the whole are really diffused through the whole, still by supporting this one point, either from above or from below, the whole mass is equally supported ; by lifting it, the whole is lifted ; by stopping it, the whole is brought to rest ; and when it rises or falls, the general mass is really rising or falling. Thus for many purposes, a body, however large, may be considered as com- pressed into or existing only in the single point called its centre of gravity or of inertia. This centre in a mass of regular shape and of uniform substance, as a ball or cube of metal, is easily found, because it is the evident centre of the form ; but in bodies that are irregular, either as to density or form, it must be found by rules of calculation hereafter explained. To say that the centre of gravity will always take the lowest situation which the support of the body will allow, is only to repeat, that bodies tend by their gravity towards the centre of the earth. In a suspended body, there- fore, as the lowest situation which the centre of gravity can find is, when it is immediately under the point of suspension, all bodies hanging freely must have their centre of gravity directly under that point. A plummet is an interesting example of this; and the truth furnishes, in many cases of irre- gular masses, a very simple practical mode of finding the centre. 86 MECHANICS. Thus if an irregular piece of plank or of pasteboard, represented here by the figure a e b d, be suspended from any point, as a, and the cord of a plummet a g be attached at the same point, the centre of gravity of the board must be somewhere in the direction of the plummet, and a chalk line left on the board where the cord touched it, must pass over the centre of gravity. If the board be then suspended by another point, as d, and another chalk line d e be made in the same man- ner, the place c, where the two lines cross or cut each other, will indicate the centre of gravity ; and the board when sup- ported by a cord attached there, will hang evenly balanced. The following cases further illustrate the truth, that the centre of gravity always seeks the lowest place. They seem at first to be exceptions to the law ; but when more fully considered, are interesting proofs of it. A wooden cylinder or roller e d c, placed on a slope or inclined plane a b, will naturally descend, because its centre of gravity is thereby approaching the earth ; but if there be a heavy mass of lead c introduced at one side, which must rise before the roller can descend, the rise of the mass being contrary to gravity, the motion will be arrested. Indeed if the roller were placed on the plane with the lead in the position d, the lead would fall down to the position c, and so would move the roller towards &, exhibit- ing the singular phenomenon of a body rolling up hill by the action of its weight. If a billiard-ball be placed upon the small ends of two billiard sticks or cues a b and c d, laid on a table with their points c and a in contact, but with the larger ends b and d so far apart that there may be just room for the ball to touch the table be- 'tween them, the ball will roll along between the cues, sinking gradu- ally from its high situation near their points, to its lower situation near b. To a careless observer, it would then have the appearance of rolling upwards, because the cues on which it rests are thicker towards the end d and b ; but it would really be descending in obedience to gravity. If a double cone, as represented at/, were substituted for the ball, it would similarly roll from c to e, and with still niore of the fallacious appearance of rolling upwards, because its ends would always be resting on the upper and rising surfaces of the cues. The board or stick c d resting on the edge of the table a b would naturally fall if left to itself, ' because more than half of it is beyond the edge of the table ; but strange to say, an additional weight e attached to its projecting part as at b by the cord b e, instead of pulling it down fast- er, shall fix or steady it on the table, provided the weight be pushed inwards a little by a rod d e resting against it and against a niche in the stick at d. It is evident that the stick c d, in falling, must turn round the edge of the table at Fig. 30. CENTRE OF GRAVITY. 87 b; but in so doing, after the arrangement now supposed, it must lift the weight e along the path e f- which rise, as the weight is heavier than the stick (that is to say, as the common centre of gravity of the connected objects is near e, ) gravity forbids, and therefore the stick and weight will both remain supported by the table. An umbrella or walking cane, hanging on the edge of a table by a crooked handle, is another instance of the same kind. And the common toy of a little man standing on tiptoe upon the top of a pillar, and supporting two leaden bullets by wires descending from his hands, is another combination of parts which places the centre of gravity of the whole the support, making the combination a kind of pendulum. By attending to the centre of gravity of the bodies around us on earth, we are enabled to explain why, from the influence of gravity, some of them are stable 'or firmly fixed, others tottering, others falling. If we find that a body, from its form or position, cannot be overturned without its centre of gravity being lifted, knowing now that the general mass is then lifted in the same degree, we see why a weak cause cannot effect the change. The rise of the centre of gravity, or body, in any case of falling over when the centre of gravity is over the middle of the sustaining base, will be proportioned to the breadth of the base of the body, compared with the height of the centre of gravity above the base. This is shown in the annexed figures of which the two particulars of base and height &rv combined in a series of proportions. In the figures, the dot c marks the place of the cen- tre of gravity, and the curved line beginning from the dot marks the path of the centre of gravity, when the body is overturned. This curved line is a portion of a circle which has^the edge or extremity of the base (Z>, in fig. A.) as a centre, because the body in turning must rest upon such extremity or corner as the centre of its motion. The farther inwards, therefore, from this extremity that the centre of gravity is, as marked by where a plumb-line as p, hanging from it, crosses the base, the farther, of course, is the centre of gravity from the top of the circle which it has to describe in moving, and the steeper, consequently, will be its commencing path j and as in the case of bodies made to roll up slopes, the steeper the ascent, the greater will be the force necessary to give motion. The line of a plummet hanging from the centre of gravity is^called the line of direction of the centre, or that in which it tends naturally to descend to the earth. In fig. A, which has a broad base and little height of the centre of gravity, we see that the centre must rise almost perpendicularly before it can fall over, and the resistance to overturning is therefore nearly equal to the whole weight of the body. Hence the firmness of a pyramid. In figures B, C, and D, progressively, the commencing path of the centre is less steep, because the base is narrower, and hence the bodies are so much the less stable. B, may represent an ordinary house, C, a tall narrow house, and D. a lofty chimney. 88 MECHANICS. Fig. E, shows a tottering position, for the centre of gravity being directly over a base which is a mere point, the least inclination places it on a descending slope, and the body- must fall. Fig. 32. K. In F, the position is tottering on one side, and stable on the other. This explains how the least inclination of a standing body virtually narrows, in one direction, its sustaining base. In Gr, which represents a ball upon a level plane, the whole mass is sup- ported on a single point, as in E, yet the body has no tendency to move, because, in any other possible position, the centre would still be as far from the sustaining plane. In moving, the centre describes the straight level- line a b. In H, the ball is on an inclined plane, and rolls down, the centre of gravity describing the oblique line b a. In I, which is an oval body resting on a level plane, when the body is moved to either side, the centre of gravity must rise, as in the case of a pen- dulum. Hence an oval body on a level will rock or vibrate like a pendulum. K, is a true pendulum, whose centre of gravity describes the curve here shown, as explained in Section II., at page 60. The importance of the subject of the centre of gravity will be farther judged of by the facts which are now to be reviewed. A cart loaded with metal or stone may go safely along a road of which one side is higher than the other, as here shown, but were the same cart loaded with wool or hay it would be overturned ; because, although the sustaining base be the same in the two cases, the line of direction falls much within it from the low centre of gravity of the metal at (^but falls very near the wheel at P, or altogether on the outside, from the high centre of the wool at a, and in the latter case the centre has offered to it a descending path. This explains why lofty stage coaches or vans are so dangerous, and particularly when heavy luggage is placed on the top, and why lofty gigs and curricles have led to so many fatal accidents. As regards any of these, a defect of smoothness or of level in the road, or even, in a case of quick driving, a slight lateral bend often suffices to produce the catastrophe. The safety-coaches of late times are made with the wheels far apart to give a broad base, and with the luggage receptacles and seats for outside passengers placed low down before and behind the body of the carriage, instead of on the top, as formerly. The feet of tripods are generally expanded below to give a broad base. The same is true of our common chairs ; but a thoughtless child often leans so far over the back of the chair, that he causes the line of the general centre of gravity to fall beyond the base, and the chair with its load is overturned. Fig. 33. CENTRE OF GRAVITY. 89 The small lofty chairs made to raise children to the parents' elbow at the dinner-table, are very dangerous if the feet are not made to spread much. Pillar-and-claw tables, candle-sticks, table-lamps, and many other articles of household furniture, have stability given in the same manner. The least inclination of a standing body virtually narrows the supporting base. This truth is explained by jig. F. It shows the necessity of building the thin walls and tall chimneys of modern houses perfectly upright. And hence the extreme importance and utility of that simple instrument, the plummet or plumb-line, which, when applied to a body, is a visible indication of the line of its centre of gravity. The mason and many other workmen cannot proceed a step without their guiding plummet. The brick walls of ordinary houses are so thin, that, to have standing strength, they require to rest against one another ; and hence they occasion- ally exhibit the kind of stability which belongs to a child's house built of cards. As contrasted with the masses of masonry which remain to us from antiquity, resting on firm-spreading basements, they are examples of what is truly ephemeral, in comparison with that which has partaken of the per- manency of nature's own works, covering regions with mighty ruins. What magnificent illustrations of strength and durability, dependent on propor- tions, are those ancient pyramids and temples, which still give such interest to the banks of the Nile, and to the valleys and plains of Asia ! There are many remarkable structures on earth which lean or incline a little } yet so long as the line of their centre of gravity remains within the base, and the parts of the mass have tenacity among themselves sufficient to hold together the structure will stand. The famous tower of Pisa was built intentionally inclining, to frighten and surprise : with a height of one hun- dred and thirty feet, it overhangs its base sixteen feet, and assumes nearly the air of fig. F. in page 88. The tall monument near London Bridge inclines so much, that in high winds, from a particular quarter, timid minds have doubted of its stability. And many of the most lofty and beautiful of our cathedral spires or tow- ers, as that of Salisbury, have lost something of their perpendicularity. An oval body on a flat level surface, as already explained by fig. I, page 88, oscillates somewhat like a pendulum, because, when disturbed from its middle position, its centre of gravity has risen and seeks to return. The same is true of any regular slice or portion of a solid globe, which will con- sequently always come to rest with its plane .face turned directly upwards. The rocking-horse of children and the common cradle are exemplifications of the same class. But perhaps the most curious instances are those rocks called Loggan or Laggan stones, of which there are several among the picturesque barriers of the British coast. An immense mass, loosened in some convulsion of nature, is found with a slightly rounded base resting on a flatter surface of rock below; and is so nearly balanced, that the, force of a man suffices to move it. Some of these have been objects of much superstitious veneration to their neighbourhood. There is an amusing Chinese toy, made in obedience to the same princi- ple. It has the appearance of a little fat, laughing man, sitting on the ground with his feet concealed under him; but where the feet should be, there is only a rounded smooth surface, with heavy lead ballast placed in it, so low, as always, when allowed, to raise the body to the erect or sitting 90 MECHANICS. attitude. A child pushes the little fellow down again and again, and would persuade him to be still, but is surprised to see him always up the moment after, shaking about and as lively as ever. The vibratory motion of a pendulum, as dependent upon the circumstance of the centre of gravity having been moved from its lowest place, which it again constantly seeks, was so fully considered in the last chapter, that it need not be again dwelt upon here ; but we have to enumerate the follow- ing phenomena as being of the same class : The vibrations of a common swing. The rocking of a balloon when it first ascends. The spontaneous shutting of those gates or doors of which the upper hinge overhangs or projects beyond the lower, causing the gate, when in the shut position, to have its lock lower than when in any other. Such a gate always returns of itself, from either side, to the shut position, just as a pen- pulum returns to the lowest part of its arc : the gate, in fact, is but a sloping pendulum. Of the same nature also is the rocking or rolling of a ship, in particular states of wind and sea. When the centre of gravity of a ship is too low, owing to all the heavy load being placed near the keel, this pendulum- motion, in rough weather, becomes excessive and dangerous. The actions and postures of animals, and particularly of man, illustrate beau- tifully the observations made above with respect to the centre of gravity. A body, we have seen, is tottering in proportion as it has great altitude and narrow base but it is the noble prerogative of man to be able to sup- port his towering figure with great firmness, on a very narrrow base, and under constant change of attitude. This faculty is acquired slowly because of the difficulty. A child does well who walks at the end of ten or twelve months j while the young of quadrupeds, which have a broad supporting base, are able to stand and even to move about almost immediately after birth. The supporting base of a man is the space occupied by and included be- tween the feet. The advantage of turning out the toes is, that without taking much from the length of the base, it adds considerably to the breadth. If there be much art in walking on two perfect feet, there is still more in walking on two slender wooden legs, with rounded extremities : which, however, we often see done, by mutilated soldiers and sailors. All the ladies of the empire of China have to acquire nearly the same talent as these victims of war,; for barbarous custom has crippled them, by confining their feet for life in such shoes as fitted them in infancy. But surpassing in difficulty any of these instances is the practice, which is general among the inhabitants of the sandy plains, called the Landes, in the south-west of France, of walking on stilts. The Landes afford tolerable pasture for sheep ; but during one portion of the year are half covered with water, and during the remainder are still very unfit walking ground, by reason of their deep loose sand and thick furze. The natives meet the incon- veniences of all seasons by doubling the length of their natural legs, through the addition to them of the stilts mentioned, which they call des echasses. Mounted on these, which are wooden poles, put on and off as regularly as the other parts of dress, they appear to strangers a new and extraordinary race of long-legged beings, marching over the loose sand, or through the water, with steps of eight or ten feet in length, and with the speed of a trotting horse ; their moderate journeys being of thirty or forty miles in a day. While CENT RE OF GRAVITY. 91 watching their flocks, they fix themselves in convenient stations by means of a third staff which supports them behind, and then with their rough sheep-skin cloaks and caps, like thatched roofs over them, they appear like little watch- towers, or singular lofty tripods, scattered over the face of the country. Still beyond the art of walking on stilts is that which some persons attain of walking and dancing on a single rope or wire ; or even of keeping the centre of gravity above the base, while standing on the moveable support of a galloping horse. A rope-dancer usually carries a long pole in his hand, to balance him ] it is loaded at each end, and when he inclines, he throws it a little towards the side required, that the reaction may restore his perpendicularity. Much art of the same sort is shown, in the attitudes and evolutions of the skater ; in the amusements of supporting a stick upright on the end of the finger ; and many other feats of a like kind. Attitudes generally depend on the necessity of keeping the centre of gravity of the body over the base under variety of circumstances, as in the straight or upright part of a man who carries a load on his head ; the leaning forward of one who carries it on his back ; the hanging backwards of one who bears it between his arms; the leaning to one side of him who is carrying a weight on the other side ; the habitual carriage of very fat people, whose head and shoulders are thrown back, giving a certain air of self-satisfaction, an air which belongs also to the expectant mother, and even to the dropsical patient, although producing in the latter so sad an incongruity. When a man walks or runs, he inclines forward, that the centre of gravity may overhang the base : and he must then be constantly advancing his foot to prevent his falling. He makes his body incline just enough to produce the velocity which he desires. A man, in pulling horizontally at a load, is merely causing his body to overhang its base, so that its tendency to fall may become a force or power applicable to the work. When a man rises from a chair, he is seen first to bend the body forward, or to draw the feet backward, so as to bring the feet or base under the centre of gravity, and then he lifts the body up. If he lifts too soon, that is, before the body be sufficiently advanced, he falls back again. A man standing with his heels close to a perpendicular wall, cannot with- out falling, bend forward sufficiently to pick up any object that lies before him on the ground } because the wall prevents him from throwing part of his body backward, to counterbalance the head and arms which must pro- ject forward. A person little versed in such matters, might agree to give ten guineas for permission to possess himself, if he could, of a purse of twenty, laid on the ground before him : he of course would lose his stake. When a man walks at a moderate rate, his centre of gravity comes alter- nately over the right and over the left foot. This is the reason why the body advances in a waving line, and why persons walking arm in arm shake each other, unless they make the movements of their feet to correspond, as soldiers do in marching. Sea Sickness is a subject closely related to the present. Man requiring, as now explained, so strictly to maintain his perpendicularity, that is, to keep the centre of gravity always over the supporting part of his body, ascertains the required position in various ways, but chiefly by comparing the perpen- dicularity, or other known position of things about him, with his own posi- 92 MECHANICS. tion. Vertigo and sickness are the consequences of depriving him of his standards of comparison, or of disturbing them. Hence on shipboard, where the lines of the masts, windows, furniture, &c. are constantly changing, sickness, vertigo and other affections of the same class are common to persons unaccustomed to ships. Many persons experi- ence similar effects in carriages, and in swings j or on looking from a lofty precipice, where known objects being distant, and viewed under a new as- pect, are not so readily recognized ; also in walking on a wall or roof; in looking directly up to a roof, or to the stars in the zenith, because then all standards disappear ; on entering a round room, where there are no perpen- dicular lines of light and shade, as when the walls and roof are covered with a paper which has no regular arrangement of spot ; on turning round, as in waltzing, or if placed on a wheel ; because the eye is not then allowed to rest long enough on any standard, &c. People when in the dark, and therefore blind people, always use standards belonging to the sense of touch ; and it is because, on board of a ship, the standards both of sight and touch are lost, that the effect is so very remarkable. But sea sickness also partly depends on the irregular pressure of the bowels among themselves and against the containing parts, when the influ- ence of their inertia and weight varies with the rising and falling of the ship. From the nature of sea sickness, as discovered in these facts, it is seen why persons unaccustomed to the motion of a ship, often find relief by keep- ing their eyes directed to the fixed shore, where visible ; or by lying down on their backs and shutting their eyes ; or by taking such a dose of exhilar- ating drink as shall diminish their sensibility to all objects of external sense. As no condition or form of matter escapes from the great laws of nature, we find the attitudes and general condition of vegetable as well as of animal bodies, characterized by the necessity of having the centre of gravity sup- ported over tho base. With what admiration may we contemplate the pine and other trees in the forests or nature, springing up to heaven as perpen- dicularly as if the plummet had been at work to direct them j and no less on the brows of precipitous hills than in the level plains. On a smaller scale, we see the grasses and corn-stalks of our fields illustrating the same truth. And whenever, in tree or shrub, accident or peculiar nature causes a devia- tion from perpendicularity, additional strength and support are provided. Beauty of form or position is often felt to exist in bodies, merely because they possess the shape and support required, that the centre of gravity may be stable. In architecture, how displeasing is a wall or pillar that is not quite upright ; or a column with too small a base ; or a very tall narrow house ; or a long slender chimney. On the other hand, how beautiful in a lofty edifice is the suitable succession of columns, from the massive Doric of the basement, supporting the whole superstructure, to the light Corinthian or kindred forms seen above. The Chinese pagoda is a fine example of the union of certain requisites for stability, viz., perpendicularity and expanding base, with the other qualities of perfect symmetry, graceful proportion, and fanciful orna- ment. When seen crowning a rising ground in a wooded island, or spring- ing up from the centre of a rich garden, it forms, perhaps, one of the most beautiful objects which fancy has ever designed. Beauty of attitude and grace of carriage in the human individual are in great part referable to the same principle. CENTRE OP GRAVITY. 93 The postures of opera dancers might pass as intentional illustrations of the number of ways in which the centre of gravity may be kept above a narrow base, by counteracting one disturbing motion or extension of a limb by some opposite and corresponding motion. The common statute of the god Mercury on tip-toe is a permanent familiar illustration of such a beautifully balanced attitude. Grace of carriage includes not only a perfect freedom of motion, but also a firmness of step, or steady bearing of the centre of gravity over the base. It is usually possessed by those who live in the country, taking much and varied exercise, or who make gymnastics a part of their discipline. What a contrast is there between the gait of the active mountaineer, enjoying the consciousness of perfect nature, and that of the mechanic or shop-keeper, whose confinement to the cell of his trade soon produces in his body a shape and air corresponding to it and in the softer sex what a difference is there, between that active and graceful fair one who recalls to us the fabled Diana of old, and that other sedentary being who, having scarcely trodden but on smooth pavements and carpets, under any new circumstances, carries her person as if it were a load quite new and foreign to her. The centre of gravity is also the centre of inertia. When a person lifts a uniform rod by its middle, the inertia of both ends being equal, he over- comes it equally, and raises them evenly together. When he lifts by a part nearer to one end, the shorter and lighter portion having less inertia will rise the first, and there will be a turning motion of the rod round the finger as a centre, proportioned to the excess of inertia in the greater side. The centre of gravity, or inertia , however, is not necessarily in the centre of the mass; for if a weight of three pounds, a, be affixed to one end of a rod, and a weight of Fig. 34. only one pound, b, be affixed to the other, the J> ^ -v two will still be balanced, if supported or lifted CD & ( "* J by a point of the rod, c, three times nearer to the ^ S centre of the large weight than to the centre of the small one. This fact is explained under the head of lever, a few pages hence. For the sake of simplicity, in describing such experiments, the weight of the connecting rod itself is neglected. The centre of gravity or inertia is also the centre of centrifugal force : for if the balls a and b of the last figure were made to spin round a common centre, as by making the connecting rod rest and turn upon a point or pivot at c; unless the point c were the centre of inertia of the two, the pivot would always be drawn in the direction of that end of the rod at which there was the greatest centrifugal force. It is on this account that in the case of a mill-stone, or great fly-wheel, or of the balance wheel of a watch, the axis must pass through the centre of inertia, to prevent its being more worn on one side than on the other. When we say in astronomy, that the earth revolves round the sun, or that the moon revolves round the earth, we do not speak with absolute correct- ness, for in all such cases, both bodies are revolving round the common cen- tre of inertia of the two. In the case of the sun and earth, as the former is about a million times larger than the latter, the common centre of inertia of the two is a million times nearer to its centre than to the centre of the earth, and is therefore within its body or circumference. The centre of inertia in a body moving evenly is also its centre of action OY percussion ; because, if such centre come against an obstacle, the whole 94 MECHANICS. momentum of the body acts there and is destroyed ; while if any other part than the centre hit, the body loses only part of its momentum, and revolves round the obstacle as a pivot or centre of motion, to pass it on the side to- wards which the greater inertia happened to 'be. In a hammer, or a bar of iron used as a hammer, or in a pendulum, the motion is not said to be even, because the velocity of the different parts is different, being greatest far from the hand or centre of motion, and the centre of all the motal inertia is nearer to the fast moving end than to the other. Its exact place, in many cases, is easily ascertained by calculation. In a uni- form rod moving as a pendulum, for instance, it is at a distance of one-third from the lower end. In the pendulum it is called the centre of oscillation. If a man use a bar or rod of iron as a hammer, he must take care to make it strike the object by its centre of action, or his own hand will receive a part of the shock. A very heavy mass thus carelessly used will seriously strain the wrist. In a common hammer, as the chief part of the matter is at the end, the centre of percussion is there too, and no precaution of the kind men- tioned is required. If a rod or small log of wood be suspended horizontally by a string tied to its middle, or be floating in water, and if a forward blow be given directly across it near to one end, the other end will be found, in the first instant to have moved a little backward, or in a direction contrary to the blow, as if the rod had been fixed upon an axis. The inertia of the general mass, by re- sisting the motion becomes in effect a Fig. 35. fixed axis. This fact is amusingly a n i illustrated by laying the ends of a long stick on two wine-glasses, and then breaking the stick by a smart downward blow of a poker on its cen- tre. Instead of breaking the glasses also, as by such a blow might be expected, the ends of the stick rise at the instant of the stroke, to turn round certain centres of resistance in the frag- ments, as at a and b , and then fall harmless on the table. In this section we have seen what admirable simplicity is given to many of our reasonings and operations, by considering bodies in reference only to their centre of inertia, under one or other of its names. u In a solid body moving about an axis, like a wheel or weighing-beam, the different parts have different velocities, according to their respective distances from the axis or centre" ( Read the Analysis. ) The truth of this proposition is perceived at pnce on comparing the motion in the rim of a wheel, or near the ends of a weighing-beam, with that in parts nearer the centres. Suppose a d to be a Fig. 36. line drawn across a wheel, or, along a weighing- beam, the centre of motion in either case being at c; then the outer circular line or path, c, which a point in a describes when moving, is longer than the "corresponding inner line, b f, which a point at b describes in the same time, as a is farther from the centre than b. This admits of easy mathematical 'demonstration, and is in- deed merely an instance of the truth, that the proportions existing between any parts or lines in one circle, hold with respect to the corresponding parts and lines in all circles. T f SIMPLE MACHINES. 95 " Hence forces with different speed may still be placed in continued connec- tion or opposition ; and they will balance or be equivalent, if the one be as much more intense than the other as it is slower." (Read the Analysis.) This is the important truth unon which the whole of mechanics may be said to hinge. It gives to man the simple machines or mechanical powers, as they have been called, the Lever, Wedge, Pulley, &c , which enable him to adapt any species and speed of power which he can command to almost any work which he has to accomplish : and the discovery of it and of means to apply it may be said to have subjected external nature to his control. His works are of a thousand kinds, from the displacing of a rock to the spinning of a delicate thread ; while the natural powers or forces at his command are chiefly wind, waterfalls, fire and animal effort and of which in any particu- lar case, he may have only one kind at his service ; still, being able to con- nect together his power and resistance by solid media, of which different parts move with any desired difference of velocities, he can employ any force for a purpose of almost any kind. There is, however, a false and most pernicious prejudice very generally existing with respect to the simple machines, which we must begin by removing, viz., that they increase the quantity of power or force applied to them. For instance, when one pound, as a at the end of a beam or lever, is seen balancing two pounds, as b, at half the distance on the other side of the axis, or four pounds as c, at a quarter of the distance, many persons be- lieve that the lever itself gives or begets a force equal to the difference of the Fig. 37. weights so balanced. But we shall now , descending far, in place of a greater * J... ! 2- :< weight descending a little way, or of an .".^ inferior force working long, instead of a | \ superior force working for a shorter '*"" time, and thus often to accomplish ends to which the force possessed would be quite unsuited if applied directly. In other words the simple machines enable us to concentrate or divide any kind or quantity of force which we possess, so as to suit it to our various purposes, just as mill-ponds and branching channels enable us to accumulate or divide the force of a stream of water; but they no more increase the quantity of power than a mill-pond increases the quantity of water. When any slender force is caused through a machine, to produce some effect which seems proportioned to an intense force, it has always to act longer, or through more space than the other, just in proportion as it is more slender; as a small stream of water acting for ten minutes, may produce the same effect as a greater gush in one minute. Twenty feet of the action of a small horse near the circumference of a great wheel, may be rendered, by intervening machinery, equivalent to ten feet of the action of a heavy ox or elephant nearer the centre. And one horse in drawing through six hundred feet, or a hundred horses in drawing through six feet, or the piston of a great steam-engine, in raising one from the bottom to the top of its cylinder, &c., may all be made to do the same work. 96 MECHANICS. To illustrate this subject farther; we shall suppose a weighing-beam x with a weight of one pound hanging at the end x ; then if a spring issuing from the fixed box at E, with uniform force of one pound, be made to push at the other end of the beam y, it will just balance the weight; and if it be in the slightest degree stronger than Fi S- 38- the weight, it will push the end of fl. the beam y down to B, and will raise / 3> 33 tne weight to F. If, instead of the single spring of one pound at the end of the beam, two such springs be A p T T ............ I / "" '""' .^ ...... -U ........ + applied at half way from the centre "Jj to the end so as to press at A, where there is just half the extent of mo- tion, or room to act, as at B, exactly the same effect will follow. Now because one spring at the end of the beam is seen here doing the same work as two similar springs, or a single spring of double strength at the middle, it might at first appear that there was a saving of power by using the single spring and longer lever ; but let it be observed, that the two middle springs have each issued from their box only one inch, while the single spring at the end has issued two inches : in both cases, therefore, exactly two inches of one-pound spring have been used. In the last experiment, pound weights or little buckets of water might be used instead of the springs, and with exactly the same result one pound or pint at the end of the arm producing the same effect as two pounds or pints at the middle of it ; but it would be observed that the single quantity fell two inches, while the double quantity at half distance fell only one inch ; and to replace them after they had done their work, there would evidently be the same labour, whether a person had to lift the single quantity first one inch, and then another, or had to lift, first, one half of the double equipoise an inch, and then the other half as much. Each atom of matter may be considered as held to the earth by its thread of attraction, a.nd if one atom rise or fall ten inches, just as much of the supposed thread of attraction will be drawn out or returned as if ten atoms rise or fall one inch. And so where a weight of one pound is made to do any work, instead of a weight of two pounds, there is no more saving than in giving away two yards of single rope instead of one yard of double rope ; and in like manner for all other differences of intensity. If a man were to exert a force of one hundred pounds at A, in the above figure, to lift the weight, a boy at B, with force of fifty pounds, might do the same work ; but the man would only have worked or pressed down through one foot, while the boy would have worked through two; and there- fore, although the boy, with the assistance of the lever, seemed to become as strong as the man, the case would merely be, again, that of the one-pound spring unbending two inches, to produce an effect equal to that of the two- pound spring unbending one inch. The boy would be using two feet of his smaller force, where the man used one foot of his greater force ; and if the work had to be long continued, the boy would have completely exhausted himself, when the man remained yet fresh. A case of the lever, exhibited in this diagram, serves well to explain the nature of mechanical powers in general. Suppose A to be a weight of four pounds at the end of a rod or lever A B, (p. 97) made to turn on c as an axis or fulcrum, and having the arm c B four times as long as the arm c A, (but the two arms of the lever being equipoised so as not to conceal the action SIMPLE MACHINES. 97 * of weights subsequently attached to them ;) then one pound at' the end B, would balance the four pounds at the end of A, and with the slightest addi- tional weight would preponderate. Now let us suppose the arc B b to have been fixed to the long arm of the lever with the four projections or shelves here shown on which balls of one pound might rest; then if one of the Fig. 39. four balls from the plane d were to roll upon the first shelf, it would just balance A, and, with one grain more, would descend to the plane e, one inch below ; then a second ball of one pound would occupy the second shelf, and would descend in the aume way, to be followed by a third, and afterwards by / "" a fourth ; and when the whole four had fallen from d to e, they would Just have lifted the four pound mass, at the other end of the lever, one inch. So that, although one pound was seen here lifting four pounds, it would only have lifted them one-fourth part as far as it fell itself, and the sum of the phenomena would be, that four pounds by falling one inch at the long end of the lever, had raised four pounds through the same distance of one inch at the short end. No mechanical power or machine generates force more than the lever does in this case. It appears, then, from all this, that as the quantity of motion in a body is measured by its velocity and the number of atoms in it conjointly, so the quantity of force exerted in any case, is measured by the intensity of the force conjointly with the space through which it moves. A clear mode, therefore, of comparing forces, is to state the lengths and the intensities for instance, to speak of ten feet of one-pound force, as equal to one foot of ten-pound force, &c. A horse pulling with the force of fifty pounds goes generally at the rate of six miles an hour ; the steam-engine piston is generally made to move at the rate of two hundred feet per minute, bearing a pressure of steam 'of about twenty pounds to each square inch of its surface ; a particular mill-stream may have a force of one hundred pounds, with a velocity of a hundred and fifty feet per minute : now it is easy, by simple arithmetic, and the rule of length and intensity above explained, to compare all these and other forces as applicable to any given work. We must warn the reader, however, that there are many important considerations connected with the practical employ- ment of forces, according to their respective nature and that of the resistance to be overcome, which cannot be entered upon in this elementary work. In very many cases there is a great waste or unavoidable loss of force, because the resistance, in yielding, runs away or escapes from the force ; as when a ship runs away from the wind which is driving her, or the floats of a quick moving water-wheel, from the stream which turned it. Horses drawing boats or carriages at the rate of five miles an hour, might exert great force, but to have a speed exceeding twelve miles they might require tl^ir whole effort to move their own bodies. As a general rule, although equul quantities of force balance each other when applied to parts of a lever or wheel altogether or nearly at rest, still when a force is made to act near its axis or fulcrum, to produce considerable velocity in a more distant part of the machinery, much of it is wasted in pressure against the fixed fulcrum. What an infinity of vain schemes yet some of them displaying great ingenuity for perpetual motion, and new mechanical engines of power, &c. ; 7 98 MECHANICS. % would have* been checked at once, had the great truth been generally under- stood, that no form or combination of machinery ever did or ever can increase, in the slightest degree, the quantity of power applied. Ignorance of this is the hinge on which most of the dreams of mechanical projectors have turned. No year passes, even now, in which many patents are not taken out for such supposed discoveries; and the deluded individuals, after selling perhaps even their household necessaries to obtain the means of securing the expected advantages, often sink into despair, when their attempts, instead of bringing riches and happiness to their families, end in disappointment and ruin. The frequency, and eagerness, and obstinacy, with which even talented individuals, owing to their imperfect knowledge of this part of natural philosophy, have engaged in such undertakings, is a remarkable phenomenon in human nature. Examples of such schemes will be noticed in different parts of this work, where they may serve to illustrate points under consideration. " Lever ) wheel and axle y &c" (Read the Analysis, at page 84.) These are the simplest of the contrivances which the circumstances of solidity in masses has enabled man to adopt for the purpose of connecting or opposing forces and resistances of different intensities. We proceed to describe them, and to explain some of their, useful applications. " Lever." A beam or rod of any kind, resting at one end of a prop or axis, which becomes its centre of motion, is a lever ; and it has been so called, probably, because such a contrivance was first employed for lifting weights. This figure represents a lever employed to move a block of stone ; a, is the end to which the power or force is applied,/, is the prop or fulcrum, and the mass 6, is the weight or resistance. According to the rule already given and explained at page 96, the power may be Fig. 40; as much less intense than the resistance as it is fajrther from the fulcrum, or moving through a greater space. A man at a, there- fore, twice as far from the prop as the centre of gravity of the stone 5, will be able to lift a stone twice as heavy as himself; but he will lift it only one inch for every two inches that he descends : and two men would be required, acting at half the dis- tance, to do the same work. There is no limit to the difference, as to intensity, of forces which may be made to balance each other by the lever, except the length and strength of the material of which levers have to be formed. Archimedes said, " Give me a lever long enough, and a prop strong enough, and with my own weight I will lift the world. " But he would have required to move with the velocity of a cannon-ball for millions of years, to alter the position of the earth by a small part of an inch. As stated in a former part of the volume, this feat of Archimedes is, in mathematical truth, performed by every man who leaps from the ground ; he kicks the world away from him when he rises, and attracts it again when he falls back. To calculate the effect of a lever, in practice, we must always take into account the weight of the lever itself, and the fact of its bending more or less ; but in expounding the theory of the lever, it is usual to consider, first, SIMPLE MACHINES. 99 what would be the result if the lever were a rod without weight and without flexibility. The rule for the lever, that the opposing forces, to balance each other, must be more or less intense, exactly as they act nearer to or farther from the centre, holds in all cases, whether the forces be on different sides of the prop or both on the same side, and whether the force nearest to the prop have the office of power or of resistance ; it holds, also, whether the lever be straight or crooked. The following are examples of levers with the prop between the forces. The handspiJce, represented in page 98, is a lever moving a block of stone* The same form, when made of iron, with the extremity formed into claws, is called croio-bar. Both kinds are used by gunners, in working cannon during battle : they are also used generally for lifting and moving heavy masses through small spaces, as the materials of the mason, the ship-builder, the warehouse-man, &c. A short crow-bar is the instrument of house-breakers, for wrenching open locks or bolts, tearing off hinges, &c. The common daw-hammer, for drawing nails, is another example. A boy who cannot exert a direct force of fifty pounds, may yet, by means of this kind of hammer, extract a nail to which half a ton might be quietly sus- pended, because his hand moves through, perhaps, eight inches, to make the nail rise one-quarter of an inch. The claw-hammer also proves, that it is of no consequence whether the lever be straight or- crooked, provided "it produces the required difference of velocity between power and resistance. The part of the hammer resting on the plank is the fulcrum. A pincers or forceps consists of two levers, of which the hinge is the common prop or fulcrum. In drawing a nail with steel forceps or nippers, we have a good example of the advantages of using a tool : 1, the nail is seized by the teeth of steel instead of by the soft fingers : 2, instead of the griping force of the extreme fingers only, there is the force of the whole hand conveyed through the handles of the nippers : 3, the force is rendered, perhaps, six times more effective by the lever-length of the handles : and 4, by making the nippers, in drawing the nail, rest on one shoulder as a fulcrum it acquires all the advantages of a lever or claw-hammer for the same purpose. Common scissors are also double levers, and those stranger shears with which, under the power of a steam-engine, bars and plates of iron are now cut as readily as paper is cut by the force of the hand. The common fire-poker is a lever. It rests on the bar of the grate as its prop, and displaces or breaks the caked coal behind as the resistance. The mast of a ship, with sails set upon it, may be regarded as a long lever, having the sails as the power, turning upon the centre of buoyancy of the vessel as the fulcrum, and lifting the ballast or centre of gravity as the resistance. For this reason lofty sails make a ship heel or lean over greatly, and if used in open boats, are dangerous. In some of the islands in the Eastern and Pacific Oceans, for the sake of sailing swiftly, boats are used so extremely narrow and sharp, that to counteract the overturning tendency of their large sails, they have an outrigger or projecting plank to wind- ward, on the extremity of which one or more of the crew may sit as a balance. Perhaps no instance of the lever, with the prop between the forces, is more interesting than the weighing -beam ; whether with equal arms, form- ing the common scale-beam ; or with unequal arms, forming the steel-yard. 100 MECHANICS. We have seen why quantities of matter attached at equal distances from the prop, must be equal to each other in order to balance. A lever, there- fore, which enables us to place quantities thus exactly in opposition to each other, and which turns easily on its axis, becomes a weighing-beam. Of this the annexed figure shows a common form. 41 - The axis or pivot at c is sharpened below, wedge-like, that the beam may turn easily, and that its centre of motion may be nicely determined ; in a delicate balance for philo- sophical purposes, the axis is almost as sharp as a knife edge, and rests on some hard smooth surface of support, so as to turn with the weight of a small part of a grain. The scales also of a weighing-beam are suspended on sharp edges to facilitate motion, and to determine nicely the points of suspension. If the two arms of a beam be not of perfectly equal length, a smaller weight at the end of the longer will balance a greater weight at the end of the shorter. An excess of half an inch in the length of a beam-arm, to which merchandise is attached, where the arm should be eight inches long, would cheat the buyer of exactly one ounce in every pound. This case might be detected instantly, by changing the places of the two things balanced ; for so, the lightest would be at the short arm, and would then appear doubly too light. A beam intended for delicate purposes, and required, therefore, to turn easily, must have its centre of gravity very near the axis on which the beam turns; for if otherwise, th because thirteen times weightier than water, would stand only about m. The shape, size, or position of the vessels in which the oppos- ing fluids might stand, would have no in- fluence on the relative heights of the surfaces ; for if we suppose a larger vessel, such as is represented here by the dotted lines between the letters e f m, to be substituted for the leg c d of the tube, the various -fluids to balance the water in b d, would have to stand just as high in it as in the smaller tube. " A body immersed in a fluid, displaces exactly its own bulk of it, which quantify having been just supported by the fluid around the body is held up with force exactly equal to the weight of the fluid displaced, and must sink or swim according as its own weight is greater or less than this" A bladder full of air, and maintaining the bulk of a pound of water, requires a force of one pound (except a few grains, the weight of the air,) to plunge it under the water. The same bulk of gold is held up in water with exactly the same force ; so that, if previously balanced at the end of a weighing beam, it appears on immersion to have lost one pound of its weight. And a piece of wood, ivory, or any other substance, having exactly the same bulk, is opposed on entering the fluid by the same resistance. The reason of thi^i is obvious, for the immersed body takes the place of water which weighed one pound and yet was supported, and whose pressure was necessary for the equilibrium of the rest. In a vessel of water repre- sented here by the figure a b, let us append to any portion of the water, a single column of particles, for instance, represented by the line c d : we know that each column is steadily supported in its place, because the particle of the liquid immediately under it is tending upwards to escape from the surrounding pressures, with force exactly equal to the weight of the column ', and what is true of a column of single particles, is true of any other portion, such as the larger column represented by the figure/ h g. If such portion weighed exactly a pound, the surface under it would be tending upward with the force of a pound ; and if the portion, without changing its bulk or form, were to become ice, it would still be exactly supported by the surface below pressing upwards with a force of a pound ; and farther, if a similar column of wood, or stone, or metal, were there, the surrounding pressure would still be the same. Again, if we suppose only half the column to be solidified, the portion h g for instance, it, would be pressed upwards with a force of one pourfd at g ; but its own weight of half a pound, and the weight of the half pound of water above it, would produce an exact balance and maintain rest. Fig. 79. J? cL 144 HYDROSTATICS. It is very important to have clear notions on this subject ; and as different minds apprehend such matters with different degrees of facility, and ill different ways, we shall state the same general truth in other words. Let us consider a mass of fluid as consisting of a vast number of extremely minute columns of single particles standing side by side, where every particle supports those above it by tendency upwards which it requires through the pressure of the fluid surrounding it. Now if we suppose the particles of a portion of a fluid mass, of any shape, to stick together, or to become ice without change of bulk or weight, that portion when solid would still be between the same forces as when fluid, and therefore would be equally supported, and would remain at rest. And if gold, or silver, or glass, or wood, having the same bulk, were substituted for the supposed ice, such new substance would still be sustained with the same force ; so that a substance of exactly the same weight as the ice or water displaced, would have no tendency either to rise or to fall more than the water itself had j but a substance heavier would sink, and one lighter would swim, and in either case with force exactly proportioned to the difference between its weight and that of an equal bulk of water. Few persons, in now reading the statement of this truth in appearance so simple and obvious would imagine that it had remained so long unknown and that the discovery of it may be accounted one of the most important which human sagacity ever made, but such is the case. We owe the dis- covery to one of the master-minds of antiquity that of Archimedes. He caught the idea one day while his limbs were resting on the liquid support of a bath : and as his God-like intellect darted into futurity, and perceived many of the important uses to which the knowledge was applicable, he is said to have become so moved with admiration and delight, that he leapt from the water, and unconscious of his nakedness, pursued his way home- wards, calling out " evgyxa, wgyxa," I have found it. He was thinking chiefly of the ready means, thus obtained, of ascertaining in all cases what has since been called the specific gravity of bodies, viz., the comparative weights of equal bulks of different substances ; as of gold, or silver, or copper, or iron, compared with water ; and in" the case of mixtures, as of gold with silver for instance, of declaring at once the proportion present of each important problems, which, until then, could not be correctly solved. The hydrostatic law now explained, has since led to great advances in various arts. It may be regarded as a chief foundation of chemistry, for by it the chemist distinguishes one substance from another, distinguishes a pure from an impure substance, and discovers the nature of many mixtures or compounds. The merchant often judges by it of the worth of his merchan- dize. In any case it enables an inquirer to ascertain at once the exact size or solid bulk of a mass, however irregular even of a bundle of twigs. It has become the cause of improvements in navigation, in marine architecture, and in many other arts. We shall now discuss more particularly the subject of comparative weights or specific gravity. 11 The force with which a body is held up in a fluid, being the exact weight of its bulk of that fluid, by ascertaining this force and comparing it with the weight of the body itself the comparative weights or SPECIFIC GRAVI- TIES are found." (Read the Analysis, p. 126.) If any b6dy, c, a mass of gold, for instance, be suspended by a thread or FLUID SUPPORT. SPECIFIC GRAVITY. 145 Fig. 80. hair from the bottom of one scale b of a weighing-beam, and be balanced by weights put into the other scale a, and if a vessel of water be then lifted under it so that the water shall sur- round it, the body is pushed up or supported by the water with force equal to the weight of the water which it displaces; the weights, therefore, then required in the scale b to restore the balance, show truly the exact weight of the water displaced ; or of water equal in bulk to the body ; and the weights in the two opposite scales show the comparative weights of the body and of its bulk of water. In the supposed case, whatever weight the gold had in the air, it would seem to lose when the water surrounded it, about a nineteenth part of such weight ; that is, the water would support it with this force ; and gold would thus be proved to be about nineteen times as heavy as water. In making- a table of specific gravities, it was necessary to select a common standard with which all other substances should be compared, and this has been done in choosing water ; the reason of preference being, that water can be so easily procured in a state of purity, and therefore of uniformity, in all situations. When we say, therefore, that gold is of the specific gravity 19, and copper 9, and cork ^, we mean that these substances are just so much heavier or lighter than their bulk of pure water in its densest state, viz., at the temperature of 40 degrees of Fahrenheit's thermometer. As the substances in nature differ as to form and other qualities, cor- responding differences have to be made in the manner of ascertaining their specific gravities : the following cases are most important. Solid bodies insoluble in water and heavier than it as the metals, &c., are merely suspended by a thread or hair, having nearly the specific gravity of water, to one scale of the hydrostatic balance (simply a good weighing- beam with a water- vessel below one of the scales ;) and the body being first balanced or weighed in the air, and then in water, as already described, the weight and the loss, represented, if the operator chooses, by the weights in the opposite scales, are the weights of equal bulks of the two substances ; and by finding, through the arithmetical operation of division, how often the weight of the water is contained in the weight of the solid, we find the specific gravity of the solid, or how much it is weightier than its bulk of water. It is almost superfluous to remark, that putting weights into the scale, b or taking them out of the scale a, are equivalent operations. We shall explain afterwards, that for very delicate purposes bodies must be weighed first in a vacuum, instead of in air, or a suitable allowance must be made ; for air itself supports a little any body immersed in it. Solids lighter than water, as cork, are weighed in it by attaching to them a mass of metal or glass heavy enough to sink them, and already balanced in water for the purpose ; or by making the line which connect them with the weighing beams pass under a small pully fixed at the bottom of the vessel, so that the rising of the end of the beam to which they are attached shall draw them down. 10 146 HYDROSTATICS. A solid soluble in water, as a chrystal of any salt, may be protected during the operation of weighing in water, by previously dipping it in melted wax, so as to leave a thin covering on it ; or it may be weighed in some liquid which does not dissolve it, allowance being afterwards made for the difference between the weight of such liquid and of water. Powders insoluble in water, such as gold dust, are weighed in a glass cup which has previously been balanced in water for that purpose. Powders soluble in water, must be weighed in some other liquid. Mr. Leslie, the highly endowed professor of natural philosophy in -the University of Edinburgh, has lately suggested a novel and ingenious mode of acertaining the specific gravity of pulverized or porous bodies j but as it can be understood only by persons acquainted with the doctrines of pneumatics, the consideration of it must come under that head. Other liquids may be compared with water in several ways. 1st. If a phial be made to hold exactly one thousand grains of distilled water, at the temperature of 40, the weight of the same measure of any other liquid is found, by simply filling the phial, and weighing it. Of sulphuric acid, for instance, such a phial will contain nearly nineteen hundred grains, while of alchohol it will receive only about eight hundred. 2d. A bulb of glass, which loses one thousand grains when weighed in water, (which thousand grains is therefore the weight of its bulk in water,) may be weighed in other liquids, and the difference of loss marks the specific gravity,* as in the last case. The bulb for this purpose may be of any size, but one which loses in water exactly one thousand grains, is preferable, from the simplicity thereby given to the calculations : This remark applies also to the phial last mentioned. 3d. A contrivance which renders the beam and scales alto- gether unnecessary, is a hollow floating bulb of glass or metal a, with a slender stalk rising from it to support the little scale or dish b, and with another stalk descending to carry the weight or weights at c, which serve as ballast to it. The whole is so adjusted that when displacing one thousand grains, or other known quantity of pure water, it shall float with a certain mark upon the upper stalk just at the surface of the water. By then im- mersing it in other liquids ancl finding how much weight must be added to, or taken from it above or below, to make it float in them at the same elevation, the comparative weights of these other liquids and of water are found : or the difference of weight which makes it float at different elevations in water, having been previously ascertained, it will only be necessary, in any other case, to note exactly its elevation ; an inch of the slender stalk may be equivalent to a difference of ten grains. This instrument is called an hydrometer. There are generally printed tables and directions, accompanying all forms of it, telling the exact import of the several indications, and the allowances to be made for temperature, &c. It may be used for weigh- ing solids as well as liquids, for if any mass be put into the saucer b, weights exactly equal to the mass must be taken out of the saucer b, or from below at c, to restore the equilibrium of the instrument. The mass may be after- wards placed at c, and weighed in water. 4th. The shortest mode of ascer- taining the specific gravities of liquids, is to have a set or series of small glass bubbles of different specific gravities, so that when they are thrown into any liquid, those heavier than it will sink, and those lighter will swim, while that one which marks its specific gravity will remain merely suspended. FLUID SUPPORT. SPECIFIC GRAVITY. 147 The bubbles must, of course be numbered, and the specific gravity of each be previously known. A common use of hydrometers is to ascertain the quality of the distilled spirits brought to market, as of rum, brandy, gin, &c. All these consist of alcohol more or less diluted with water; and' duty or tax is levied upon them in proportion to their strength, or the quantity of alcohol which they con- tain. A delicate hydrometer discovers this at once. A shop-keeper in China sold to the purser of a ship, a quantity of distilled spirit according to a sample shown ; but not standing in awe of conscience, he afterwards, in the*privacy of his store-house, added a certain quantity of water to each cask. The spirit having been delivered on board^ and tried by the hydrometer, was discovered to be wanting in strength. When the vendor was charged with the intended fraud, he at first denied it, for he knew of no human means which could have made the discovery ; but on the exact quantity of water which had been mixed being specified, a superstitious dread seized him, and having confessed his roguery, he made ample amends. On the instrument of his detection being afterwards shown to him, he offered any price, for what he foresaw might be turned to great account in his trade. The specific gravity of aeriform substances is ascertainnd by means of a glass flask of known size, furnished with a stop-cock. It is first weighed when emptied by the air-pump, and afterwards when filled successively with water and with different airs or gases. Comparison of the weights gives the specific gravities, as already described. The following table shows, in round numbers, the comparative weights or specific gravities of some common substances. Water is the standard kept in view, and any equal bulk of another substance is heavier or lighter than water, according to the numbers severally attached to them. Common Salt, . . .2 Brick .... 2 Alcohol . . . S Cork . Atmospheric Air Hydrogen Gas . Platinum . . . . 22 f Gold 19i Mercury . . . . 13 Copper .... 8f Steel and Iron . . .8 Diamond . . . 3J Glass 3 Common stones . . 2$ Complete tables are found in systems of Dictionaries of Chemistry. A cubic foot of water happens to weigh very nearly one thousand ounces avoirdupois, or 62 ? pounds. Hence, in the foregoing table, the figures denoting the specific gravities tell how many times a thousand ounces of the different substances a cubic foot contains. Of gold, for instance, a cubic foot contains more than nineteen thousand ounces, being worth in money about 63,000 sterling. A cubic foot of common air contains only a little more than one ounce ; and of hydrogen gas, the lightest of ponder- able things, a cubic foot contains less than a drachm. The following facts are also illustrations of the truth, that a body immersed in a fluid is held up, or has its entrance resisted, with force equal to the weight of the quantity of fluid which it displaces. A stone which on land requires the strength of two men to lift it, may be lifted and carried in water by one man. There are cases, therefore, where 148 HYDROSTATICS. the support of water thus rendered useful, is equivalent to the assistance of additional hands. A boy will often wonder why he can lift a certain stone to the surface of water, but no farther. The invention of the diving-bell in modern tirade, having enabled men, in the building of piers, bridges, &c., to work under water almost as freely as above, many have experience of this influence of water: but workmen are- generally surprised at first, to find that below they can move much larger and heavier stones than they can in the air. Some had supposed the fact accounted for by saying that the denser air of the diving-bell, when received into the lungs gave greater strength. In recovering property from a sunken ship by the diving-bell, everything is found to be lighter in the proportion now stated. This law explains also why stones, gravel, sand and mud, are so easily moved by waves and currents. Many people expressed astonishment, in March, 1825, to learn that at the Plymouth Breakwater, the storm had dis- placed blocks of stone of many tons weight ; but we now see that the moving water had only to overcome about half the weight of the stone. When a person lies in a bath, the limbs are so nearly supported by the water as to require scarcely any exertion on the part of the individual. When this softest of all beds has been indulged in for half an hour or more, the person, on first lifting a limb out of the water, feels surprise at its great apparent weight. The workers about diving-bells always experience the sensation now spoken of, on returning to the air. The bodies of most fishes are nea'rly of the specific gravity of water, and, therefore, if lying in it without making exertion, they neither sink nor rise very quickly. When this subject was less understood, many persons believed that fishes had no weight in water; and it is related as a joke at the expanse of philosophers, that a king -having once proposed to his men of science to explain this extraordinary fact, many profound disquisitions came forth, but not one of the competitors thought of trying what really was the fact. It was beneath the dignity of science in those days to make an experiment. At last a simple man balanced a vessel of water in scales, and on putting a fish into the water, showed its scale preponderating just as much as if the fish had been weighed alone. In the sense now explained, water is said to have no weight in water. The least force will raise a bucket of water from the bottom of a well to the surface; but if the bucket be lifted at all farther, its weight is felt just in proportion to the part of it which is above the surface. " A body lighter than its bulk of water will float, and with force propor- tioned to the difference." (Read the Analysis, p. 126.) * The reason"of this is clear. If any body, the cylinder abed for instance, be partially immersed in water, we know that tHe upward pressure of the water on the bottom c d, ia exactly what served to support the water displaced by the body, viz., water of the bulk, efc d. The body, therefore, that it may remain out as far as here represented, must have exactly the weight of the water which the immersed part of it dis- places ; and if it be lighter than this, it will rise farther ; if heavier, it will sink farther until the exact balance be produced. FLUID SUPPORT. SWIMMING. 149 Hence of any body which floats in water, a pound weight displaces just a pound of water, whether the body be very light in proportion to its bulk, as cork, or heavier, as a piece of dense wood. This is experimentally shown by putting such bodies to float in a vessel originally full of water. The water displaced by each must run over the. sides of the vessel, and may be caught and measured. Hence a porcelain basin weighing four ounces will sink in water only as far as a similar wooden basin or bowl of the same weight ; and the weight of either basin may be in the substance of which it is formed, or in anything else put into it as a load. Hence a boat made of iron floats just as high out of water as a boat of simi- lar form and size made of wood, provided the iron be proportionately thinner than the wood, and therefore not heavier on the whole. An empty metallic pot or kettle is often seen floating with a great part of it above the surface of the water. Prejudice for a long time prevented iron boats from being used, although, for various purposes, they are superior to others : and there are still people who would fear to go on board of a ship built of the strong and singu- larly durable Indian teaks, because it is heavier than water, and, in the form of a log, therefore, sinks in water. Many fine ships of the line, however, and East-Indiamen of fifteen hundred tons or more, are now built of teak. Hence a ship carrying a thousand tons weight will draw just as much water, or float to the same depth, whether her cargo be of cotton or of lead : and the exact weight of any ship and her cargo may be determined by find- ing how much water she displaces. In canal boats, which are generally of a simple form, this truth affords a ready rule for ascertaining the quantity of their load. The human body, in an ordinary healthy state with the chest full of air, is lighter than water. If this truth were generally and familiarly understood, it would lead to the saving of more lives, in cases of shipwreck and in other accidents, than all the mechanical life-preservers which man's ingenuity will ever contrive. The human body with the chest full of air naturally floats with a bulk of about half the head above the water, having then no more tendency to sink than a log of fir. That a person in water, therefore, may live and breathe it is only necessary to keep the face uppermost. The reason that in ordinary accidents so many people are drowned who might easily be saved, are chiefly the following : 1st. They believe that the body is heavier than water, and therefore, that continued exertion is necessary to keep it from sinking; and hence, instead of lying quietly on the back, with the face upwards, and with the face only out of the water, they generally assume the position of a swimmer, in which the face is downwards, and the whole head has to be kept out of the water to allow of breathing. Now, as a man cannot retain this position but by con- tinued exertion, he is soon exhausted, even if a swimmer, and if he is not, the unskilful attempt will scarcely secure for him even a few respirations. The body raised for a moment by exertion above the natural level, sinks as far below it when the exertion ceases; and the plunge, by appearing the commencement of a permanent sinking terrifies the unpractised individual, and renders him an easier victim to his fate. To convince a person learn- ing to swim of the natural buoyancy of his body, it is a good plan to throw an egg into water about five feet deep, and then desire him to bring it up again. He discovers that instead of his body with the chest full of air na- 150 HYDROSTATICS. turally sinking towards the egg, he has to force his way downwards, and is lifted again by the water as soon as he ceases his effort. 2d. They fear that water entering by the ears may drown, as if it entered by the nose or mouth, and they make a wasteful exertion of strength to pre- vent it ; the truth being, however, that it can only fill the outer ear, as far as the membrane of the drum, where its presence is of no consequence. Every diver and swimmer has > his ears thus filled with water, and cares not. 3d. Persons unaccustomed to the water, and in danger of being drowned, generally attempt in their struggle to keep their hands above the surface, from feeling as if their hands were imprisoned and useless while below ; but this act is most hurtful, because any part of the body held out of the water, in addition to the face which must be out, requires an effort to support it, which the individual is supposed at the time ill able to afford. 4th. They do not reflect, that when a log of wood or & human body is floating upright, with a small portion above the surface, in rough water, as at sea, every wave in passing must cover it completely for a little time, But again leave its top projecting in the interval. The practiced swimmer chooses this interval for breathing. 5th. They do not think of the importance of keeping the chest as full of air as possible ; the doing which has nearly the same effect as tying a blad- der of air to the neck, and without other effort, will cause nearly the whole head to remain above the water. If the chest be once emptied, while from the face being under water the person cannot inhale again, the body remains specifically heavier than water, and will sink. When a man dives far, the pressure of deep water compresses, or dimi- nishes the bulk of the air in his chest, so that, without losing any of that air, he yet becomes really heavier than water, and would not again rise, but for the exertion of swimming. The author of this work once saw a sailor ( a fine-bodied ^West India negro ) fall into the calm sea from a yard-arm eighty feet high. The velocity on his reaching the water was so great, that he shot deep into it, and, of course, his chest was compressed as now explained : probably also the shock stunned him, for although he was an excellent swimmer, he only moved his 'arms feebly once or twice, and was then seen gradually sinking for a long time afterwards, until he appeared only as a black and distant speck, descending towards the unknown regions of the abyss. Every person need not learn to swim ; but every one who makes voyages should have practiced the easy lesson of resting in the water with the face out. The head, from the large quantity of bone in it is a heavy part of the body, yet, owing to its proximity to the chest, which is comparatively light, a little action of adjustment with the hands, easily keeps it uppermost ; and there is an accompanying motion of the feet, called treading the water, not diffcult to learn, which suffices to sustain the entire head above the* surface. Many of the seventy passengers who were swallowed up on the sudden sink- ing of the Comet steam-boat near Greenock, in November, 1825, might have been saved by the boats, which so soon went to their assistance, had they known the truth which we are now explaining. A. man having to swim far, may occasionally rest on his back for a time, and resume his labor when he is somewhat refreshed. So little is required to keep a swimmer's head above water, that many individuals, although unacquainted with what regards swimming or floating, have been saved after shipwreck, by catching hold of a few floating chips or broken pieces of wood. An oar will suffice as a support to half a dozen FLUID SUPPORT. STABILITY. 151 people, provided no one of the number attempts by it to keep more than his head out of the water; but often, in cases where it might be thus serviceable, from each person wishing to have as much of the security as possible, the number benefitted is much less than it might be. The most common contrivances, called, life-preservers, for preventing drowning, are strings of cork put round the chest or neck, or air-tight bags applied round the upper part of the body, and filled, when required, by those who wear them blowing into them through valved pipes. On the great rivers of China, where thousands of people find it more con- venient to live in covered boats than in houses upon the shore, the younger children have a hollow ball of some light material attached constantly to their necks, so that, in their frequent falls overboard, they are not in danger. Life-boats have a large quantity of cork mixed in their structure, or of air-tight vessels of thin copper or tin plate : so that, even when the boats are filled with water, a considerable part still floats above the general surface. Swimming is much easier to quadrupeds than to man, because the ordi- nary motion of their legs in walking and running is that which best supports them in swimming. Man is at first the most helpless of creatures in water. A horse while swimming can carry his rider with half the body out of the water. Dogs commonly swim well on the first trial. Swans, geese, and water-fowls in general, owing to the great thickness of feathers on the under part of their bodies, and the great volume of their lungs, and the hollowness of their bones, are so bulky and light, that they float upon the water like stately ships, moving themselves about by their webbed feet as oars. A water-fowl floating on plumage half as bulky as its naked body, has about half that body above the surface of the water ; and similarly a man reclining on a floating mattrass, as in the hydrostatic bed afterwards to be described, has nearly as much of his body above the level of the water- surface, as he forces of the mattrass under it. His position, therefore, depends on the thickness of the mattrass. A man walking in deep water may tread upon sharp flints or broken glass with impunity, because his weight is nearly supported by the water. But many men have been drowned in attempting to waae across the fords of rivers, from forgetting that the body is so supported by the water, and does not press on the bottom sufficiently to give a sure footing against a very trifling current. A man, therefore, carrying a weight on his head, or in his hands held over his head, as a soldier bearing his arms and knapsack, may safely pass a river, where, without a load, he would be carried down the stream. There is a mode practised in China of catching wild ducks, which requires that the catcher be well loaded or ballasted. The light grain being first strewed upon the surface of the water to temp them, a man hides himself in the midst of it, under what appears a gourd or basket drifting with the stream, and when the flock approaches and surrounds him, he quickly obtains a rich booty by snatching the creatures down one by one adroitly making them disappear as if they were diving, and then securing them below. Each bird becomes as a piece of cork attached to his body. Fishes can change their specific gravity, by diminishing or increasing the size of a little air-bag contained to their body. It is because this bag is situated towards the under side of the body, that a dead fish floats with the belly uppermost. Animal substances, in undergoing the process of putrefaction, give out much aeriform matter. Hence the bodies of persons drowned and remaining 152 HYDKOSTATICS. in the water, generally'swell, after a time, and rise to the surface, again to sink when the still increasing quantity of air shall burst the containing parts. A floating body sinks to the same depth whether the mass of fluid supporting it be great or small : as is seen when a porcelain basin is placed first in a pond, and then in a second basin only so much larger than itself that a spoonful or two of water suffices to fill up the interval between them. One ounce of water in the latter way may float a thing weighing a pound or more, exhibiting another instance of the hydrostatic paradox : And if the largest ship of war were received into a dock, or case, so exactly fitting it that there were only half an inch of interval between it and the wall or side of the containing space, it would float as completely, when the few hogsheads of water required to fill this little interval up to its usual water- mark were poured in, as if it were on the high sea. In some canal locks, the boats just fit the place in which they have to rise and fall, and thus the expense of water at the lock is diminished The preceding examples of floating are all illustrations also of the truth that the pressure of a fluid on any immersed body is exactly proportioned to the depth and extent of the surface pressed upon. The lateral pressures just balanced one another, and the upward pressure has to be balanced by the weight of the body. Similar reasoning to that which proves that the whole weight of a body acts as if lodged in the point called its centre of gravity, proves that the whole buoyancy of a body, or the upward push of the fluid in which a body is immersed, acts as if lodged in the point which was the centre of gravity of the fluid displaced. This point, consequently, is called the " centre of buoyancy." A floating body, to be stable in its position, either must have its centre of gravity below the centre of buoyancy in which case it resembles a pendulum ; or it must have a very broad bearing on the water, so that any inclination may rause the centre of gravity to ascend in which case*it resembles a cradle or rocking-horse. Hence arises, in the stowing of a ship's cargo, the necessity of putting the heavy merchandise underneath, and generally of putting iron ballast under all the merchandise. Hence, also, the danger of having a cargo or ballast which is liable to shift its place. A ship loaded entirely with stones, is sometimes lost by a wave making her incline for a moment so much that the load ships to one side, which is then kept down. For a similar reason, a cargo of salt or sugar has a peculiar danger attached to it, for if the ship leak, the cargo may be dissolved, and then pumped out with the bilge water, leaving her with altered trim. In a fleet coming home from India, in 1809, four fine ships disappeared during a hurricane off the isle of France, and from what happened to the other ships that were saved, the cause of the destruc- tion was supposed to be, that the saltpetre of the cargoes had been dissolved and pumped out, and that the ships in consequence became unmanageable. Bladders used by beginners in swimming are dangerous, unless secured so as not to shift towards the lower part of the body. A great inventor (in his own estimation) published to the world, that he had solved the important problem of walking safely upon the water ; and he invited a crowd to witness his first essay. He stepped boldly upon the wave, equipned in bulky cork boots, which he had previously tried in a butt of water at home ; but it soon appeared that he had not pondered sufficiently on FLUID SUPPORT AMONG FLUIDS. 153 the centres of gravity and of floatation, for in the next instant all that was to be seen of him was a pair of legs sticking out of the water, the movements of which showed that he was by no means at his ease. He was picked up by help at hand, and, with his genius cooled and schooled by the event, was conducted home. Some soldiers once finding a few cork/ac&efe, among old military stores, determined to try them j but mistaking the shoulder straps for lower fastenings, they put them on as drawers^nd on then plunging in, with the hope of being able to sit pleasantly on th *water, their heavy heads went down, and they were nearly drowned When, on the return of summer, the ice breaks up in the polar regions, immense islands of it are set afloat, rising high into the air and sinking deep into the sea. The melting process, in most cases, does not go on equally in the water and in the air, and from the mass, consequently, changing form, its * stability is often lost, and one of the grandest phenomena in nature follows the overturning of a mountain the sudden subversion of an island pro- ducing a tumult in the ocean around, felt often at the distance of many leagues. The phenomena of pressure, floating, &c., in fluids, vary in proportion to the weight or specific gravity of the fluid. A ship draws less water, or swims lighter, by one thirty-fifth, in the heavy salt-water of the sea than in the fresh water of a river : and for the same reason a man swimming supports hmiself more easily in the sea than in a river. Many kinds of wood that float in water will sink in oil. A man floats on mercury as the lightest cork floats on water, and with practice he might be able to walk upon mercury. Had the water of our ocean been but a little heavier than it is, men after shipwreck might have died of famine and cold, but would not have been drowned Oil floats on water, but sinks in alcohol or aether. The term proof spirit means spirit light enough for oil to sink in it. The strength of spirit is proportioned to its lightness. Cream rises in milk, and forms a covering to it. Blood, allowed to rest after flowing from the living body, separates into parts or layers, which arrange themselves according to their specific gravities. The buffy coat of inflammation (where this exists) is uppermost, forming the surface of the general coagulum : towards the lower part of the coagulum there is an accumulation of red globules; and-the whole of the solid part floats in the serum, which is therefore lowest of all. When the red globules escape from the coagulum, they fall to the bottom even of the serum. Wine, if slowly and carefully poured on water, will float upon it. In a vessel shaped like a common sand-glass, only with a larger opening between the chambers at c, if wine be put into the Fig. 83. under chamber, and water into the upper, the two liquids will gradually change places : and if the lower half of the glass be covered, so as to leave the upper half with the appearance of a simple goblet, the water will seem to have been changed into wine. The liquids are less mixed, and change places sooner, when there is a tube 6 to carry the water down to the bottom without touching the wine, and a tube a to carry the wine directly to the top. Mercury, water, oil, air, and some other fluids may all be shaken together in the same vessel, and on standing will separate again and arrange themselves in the order of their specific gravities. 154 HYDROSTATICS. When, in a mass of water, part of it is heated more than the rest, that part, by its expansion, becomes specifically lighter than the rest, and rises to the surface. Hence, wh^n heat is applied to the bottom of a vessel containing water, a circulation is established, which goes on from the first moment until the operation of heating finishes : water is always rising from the hotter parts of the vessel, and descending over the colder parts. In like manner, when a tall glass containing hot water is dipped into cold water, a downward currem lakes place within the glass near the sides all round, and there is an upward current in the middle. This motion may be rendered very obvious by small portions of amber thrown into the water, for these being nearly of the specific gravity of water, rise and descend with it. On account of the current established in such cases, heat applied to the bottom of a vessel of liquid is soon equally diffused over it ; but heat applied at the top is there confined, because the heated and lighter fluid does not descend. Water may be made to boil at its surface, while a piece of ice lies at the bottom. The converse is impossible. The current in a fluid, produced by local change of temperature, is an important part of the following process, which the author deems applicable to various useful purposes. Heat may be transferred from one liquid to another, without mixing them, by making the hot liquid descend in a very thin metallic tube, through the cold liquid rising around it in a larger tube, Boiling water from the vessel e, for instance, may descend slowly by the small tube ea bf, which is sur- Fig. 84. rounded from a to b by cold water ascending through the tube c g. Then, as the tem- perature of two liquids, brought so nearly into contact with each other, will not, after a very short time, differ, in any one place more than a few degrees, it fol- lows that the water lately cold, will on leaving the part of the tube g, which is in contact with the boiling water descending di- rectly from e, be nearly boiling, while the water lately hot will, on leaving the tube at &, which is in contact with cold water just arrived from A, be itself nearly cold j and thus equal quantities of hot'and cold water will have exchanged temperatures. *The flux of the hot water is to be regulated by a cock 6, and that of the cold water by a cock h. The water in the part of the tube c g d rises, because it is hotter and therefore specifically lighter than that in the part h c. The author believes that an apparatus made on this principle, with an arrangement of many thin flat tubes instead of a single large tube, for the descending fluid, and a spacious box c g to contain these and the rising fluid, would be an excellent refrigera- tor in a distilling apparatus, and for cooling the wort of brewers ; or would serve as a means of diminishing the expense of warm baths, by transferring the heat from the water lately used to pure water. In distilling, the wash or low wines, about to enter the still, might be used as the cold condensing fluid to surround the warm or vapor tubes, and thus, without expense, would be FLUID SUPPORT AMONG FLUIDS. 155 heated in its progress to the still. Half the original expense of a great porter brewery is in the construction of the numerous water-tight floors on which the hot wort is thinly spread to cool. The practice of warm bathing, so conductive to health, is less common in this country, because the present expense is so great. It is a general truth in nature, that substances contract in size as they cool. There is, however, in water, a curious exception to this rule, which, operating through the principle of specific gravities, effects most important purposes in the economy of nature. Water contracts only down to the temperature of 40 deg., below which, towards 32 deg., or the freezing point, it goes on dilating again, and as ice is much lighter than as a fluid. Ice, therefore, floats on the surface of water, and being a very slow conductor of heat, defends the water underneath from the cold air, and preserves it liquid, and a fit dwelling for the finny tribe, until the return of the mild season. And not only is the extreme of cold below thus prevented, but because very cold water remains floating on the surface of a wintry lake, as cream floats on milk, it preserves underneath that warmth which is agreeable to the fishes, just as very hot water in summer remains uppermost, preserving underneath an agreeable coolness. By the dilation of very cold water, then, and the formation of ice, nature has prepared a winter garb for the inhabited lakes and rivers, as complete and effectual as for terrestrial animals, by the periodical thickening of their wool or fur. Had ice become heavier than water, so that it must have fallen to the bottom, and have left the surface without protection, a deep lake in European winters, would have been frozen into a solid lifeless mass, which summer suns would no more have melted than they now do the glaciers of Switzerland. But for this important ex- ception, therefore, to a general law of nature, many of the now most fertile and lovely portions of the earth's surface would have remained for ever barren and uninhabited wastes. 156 PNEUMATICS. PART III. THE PHENOMENA OP PLUIDS SECTION IL--PNEUMATICS. ANALYSIS OF THE SECTION. In aeriform fluids, that is, in such as have their particles held far apart by mutual repulsion, which yields, however, to any force applied, so that the mass suffers great change of volume under different degrees of com- pression. the phenomena are modified by the GREAT LIGHTNESS and ELASTICITY of the fluids, but are still in strict accordance with the general properties of fluids already explained, viz., PRESSURE EQUAL IN ALL DIRECTIONS PRESSURE AS THE DEPTH LEVEL SURFACE, and FLUID SUPPORT. The pressure of air, in all directions, and as the depth, may be studied in the effects of our atmosphere on solids on liquids : or ichen it concurs with heat, in producing the phenomena of boiling, evapo- ration, clouds, rain, dew, &c. ; or when, by varying in degree, it allows certain substances to exist sometimes in the liquid and sometimes in the aeriform states. The fluid support in air is exemplified by ballons, the ascent of flame, and smoke", winds, &c. WHATa change has taken place in the degree of man's knowledge of nature, since philosophers thought that air was one of four primary elements, viz., air, fire, water, and earth, of which all things were composed, and each of which was for ever distinct from the others. We now know that air or gas is merely an accidental state, in which any body may exist, according to the quantity of heat pervading it: the body being solid when the absence of heat allows its atoms to obey freely their mutual attraction, and to cohere as in ice, for instance ; being liquid, when so much heat is present as nearly to balance the attraction, and to let them slide freely among each other as they do in water ; and being aeriform when still more heat is added, causing the atoms mutually to repel and dart asunder to a great distance as they do in steam. But in any one of these three states, the various substances are as much themselves as in the others, and at the command of the chemist will assume any of the forms which he desires, As most substances in nature have a different relation to heat, there are some which, at the medium temperature of our earth are solid, some which are liquid, and some aeriform. The solids, in general, are the heaviest under a given volume, and therefore sink down and form the great mass or centre of the earth j the liquids follow next in order, and float upon this solid centre, filling up its inequalities with AERIFORM FLUIDS. 157 a level surface, so as to constitute the ocean ; while the airs are the lightest of all, and as a second ocean, rest above the sea and above the highest moun- tain, to an elevation of about fifty miles. Among the substances whose relation to heat causes them, when not restrained in certain combinations, to assume the form of air at very low temperatures, there are two in particular, viz., oxygen and nitrogen, which are very abundant in nature in such uncom- bined state, and of these, therefore, the atmosphere chiefly consists ; but smaller portions of almost every other substance are found in it. Water, among the supplementary matters, is much more abundant than any of the others, and in various states of cloud, mist, rain, dew and snow, it answers a thousand useful purposes, and serves beautifully to vary the scenes of nature. The atmosphere is about fifty miles high or deep, and therefore, in relation to the bulk of the earth, is as a covering of one-tenth of an inch in thickness to a common library globe of a foot in diameter. The atmospheric ocean is the great laboratory in which most of the actions of life go on, and on the composition of which they depend. A human being requires for breathing a gallon of fresh air every minute, dying equally if deprived of air, or if confined to the same. All other animals also require fresh air, but in various proportions. And in the vegetable creation, the beautiful green leaf and delicate flower are merely broad and tender expan- sions of surface for the contact of the vivifying air. Animals give out to the atmosphere a substance which vegetables absorb, and vegetables, by the absorption, fit the air again for the use of animals ; so that, upon the whole, in the various changes of nature, there is a perfect balancing of actions, which preserves the atmospheric mass in a uniform state, constantly fit for its admirable purposes. While the ancients had that notion of air, which made them apply to it vaguely, and almost indifferently, the names of air, ether, spirit, breath, life, &c., they never* dreamed of making experiments upon it, with a view to prove its relation to common matter : and one of the most beautiful portions of the modern history of man's progress in knowledge, is that which exhibits the light gradually breaking in upon this most interesting subject. Galileo was led to conclude that air made a definite pressure upon things at the surface of the earth ; Torricelli and Pascal proved that this was occasioned by its weight, and hence, moreover, they deduced the height of the aerial ocean ; Priestly, Black, Lavoisier, and others, discovered that air might be united with a metal, so as to increase its weight, and to produce a compound of totally new qualities, for they showed that many of the ores of our mines are merely metals concealed, by being thus united with a substance which, when set free, ascends as one of the ingredients of the atmosphere. They at last analyzed the atmosphere itself, and exhibited its two ingredients as distinct substances. And within a few years the nature of air or gas has been so thoroughly investigated, that we can now take a little of many a light, invisible, impalpable fluid such as we breathe, and squeezing the heat out of it by strong pressure, can make its particles collapse from their aeriform distances to assume the state of a tranquil fluid; which may then be retained as such for ever, or may be decomposed and made solid in combination with other bodies, or may be again set at liberty. The suspicion once excited, that air was as much a material fluid as water, only much less dense, by reason of a greater separation and repulsion of the particles, it was easy to follow out the parallel, and to confirm the supposition by .reference to the commonest facts. Thus, a leathern sack or pouch, opened and dipped into water so far as to become full, if its mouth be then carefully 158 PNEUMATICS. closed, retains the water, and its sides cannot afterwards be pressed together : a similar sack or bladder, opened out, and then closed in air, is found to remain, in a corresponding way, bulky and resisting, and forms what is called an air-pillow. The motion of a flat board is resisted in water : the motion of a fan is resisted in the air. Masses of wood, sand, and pebbles, are rolled along or floated by currents of water : chaff, feathers, and even rooted trees are swept away by currents of air. There are mills driven by water ; and there are mills driven by the wind. Oil set free under the surface of water, or placed there in a bladder, rises to the surface : hot air or hydrogen gas placed in a balloon, rises in the air. A fish moves itself by its fins in water : a bird moves itself by its wings in the air ; and as on taking the water from a vessel in which a fish swims, the creature falls to the bottom, gasps a few moments, and dies, so, on exhausting the air from a vessel in which birds or butterflies are enclosed, their useless wings may flap ; but they sink to the bottom, and if the cruel experiment be continued, they soon become motionless and forever. We proceed now to prove that air or gas, as a fluid, differs from the other fluids, which we call liquids, only in the two circumstances of great lightness or rarity, and of being very extensively elastic, that is to say, the particles being so related, that pressure brings them much more nearly into contact, and on ceasing, allows them to regain their former distance. Lightness of Air. The lightness or rarity of atmospheric air, as it is found on the general gurface of the earth, is such, that if, by the action of a pump, a bag of it holding a cubic foot be emptied into the copper ball of an air-gun, the ball weighs about an ounce and a quarter more than before. The same volume of water weighs nearly a thousand ounces j so that common air is about eight hundred times lighter than water. Other gases, or substances in the aeri- form state, have their various specific gravities, just as the same substances have when liquid or solid. Thus water in the form of air, that is to say, when existing as steam, and of the common density, is little more than half as heavy as the same bulk of common air \ hydrogen is only one-fourteenth part as heavy : and carbonic acid gas, which is the air that rises out of soda- water, brisk ale, champagne wine, &c., is so much heavier, that even in the atmosphere it may be poured out of one open vessel into another, as a liquid might, or, more exactly, as water might be poured out under oil. Elasticity of Air. A small bladder full of air may be pressed or squeezed between the hands so as to be much reduced in size, but on being relieved from the Fig. 85. pressure, it will immediately resume its former bulk. d, If a metalic tube or barrel of perfectly uniform bore a b, be fitted with a moveable plug or piston c, which is covered with leather and oiled, so as to slide up and down without allowing the air to pass by its sides, the air between the piston and the close bottom b may be compressed to a hundredth or less of its usual bulk ; but when allowed, will push the piston back again with the same force as it opposed to the condensation, and will recover the volume which it had before the experiment. Again, if the plug, at the commencement of the experiment, were only an inch from the bottom, enclosing air of the usual density, on drawing it up to the top, the inch of air beneath it ELASTICITY OF AIR. 159 would expand so as to occupy the whole tube, having become, of course, proportionally less dense. To the question why the air, which admits of such various density, is found to have that certain degree of it met with at the surface of the earth, we answer, that as the water, in any place near the bottom of the ocean, is pressed with force exactly proportioned to the quantity of water above it, so the air at the surface of the earth bears the pressure of the superincumbent mass of air, and on account of its extensive elasticity, suffers, like the lower- most bags of cotton or wool in a great heap, that degree of compression which the superincumbent mass is calculated to produce. We shall see below that the density of the air near the earth is changing with every circumstance which affects the weight of the atmosphere above, as winds, clouds, rain, &c., and that it bears relation to the altitude of the place of observation above the level of the sea. The tube with its piston, described in the last page, becomes, according to the position of its valves, either a syringe for injecting and condensing air, or a pump for exhausting or removing it from any vessel ; both opera- tions depending on the elasticity of air. A barrel and piston is a condensing syringe, when in a passage of com- munication between the bottom of the syringe and a receiving vessel, there is a flap or valve allowing air to pass towards the receiver but not to return. The piston, therefore, at each stroke, forces what the barrel contains of air into the receiver. When the piston is lifted again after the stroke, air re-enters the barrel from the atmosphere, either through a valve in the piston, or through a small hole near the top of the barrel. That useful contrivance, a valve, for whatever purpose used, and in whatever way formed, is in principle merely a moveable flap, placed on an opening, against which it is held by its weight, or by some other gentle and yielding force. Such a flap, it is evident, will allow fluid to pass only in one direction, viz., out- wards from the opening, for any fluid tending inwards must shut the flap, and press it the closer, the greater the tendency. To convert a forcing syringe or pump into an exhausting syringe or pump, commonly called an air-pump, it is only necessary to reverse the position of the valves ; then, on the descent of the piston, all the air between it and the bottom, instead of entering the vessel or receiver, as in the last case, escapes by a valve in the piston itself towards the atmosphere, and on the rising of the piston, a perfect vacuum would be left under it, but that the valve below, then opened by the elasticity of the air in the receiver, allows a part of that air to follow it. Thus, at each stroke, a quantity of the air, proportioned to the size of the pump, is removed from the receiver. In a good air-pump, there are two similar pumping barrels, as a and 6, to quicken the operation of exhausting ; and both are worked at the same time by the reciprocating winch or handle f } with jts pinion e, acting on the teeth of the piston rods d Fig. 86. 160 PNEUMATICS. and c. This double construction has the farther advantage, that the atmo- spheric pressure, if fifteen pounds per square inch on the upper surface of either piston, and which for a single piston would have to be overcome by the worker in lifting it, as here balanced always by the corresponding pressure on the other piston. Both pumps communicate with the tube g h, which at h rises tightly through the round plate of the machine to i. This flat plate is so smooth, that a glass bell or receiver &, with a smooth ground lip, when placed upon it, forms an air-tight joining. On working the pump, such a bell is exhausted of its air, and fitted for showing the many interesting phenomena which the air-pump can display, and which will pass under review as we proceed. The supporting frame-work of the pump is not shown here. The law of the elasticity of air is, that its spring, or resistance to compres- sion, increases exactly with its density or the quantity of it collected in a given space. Hence, by finding in any case either the density of the air, or the spring, or the compressing force, we know all the three. It has been ascertained by experiments described a few pages farther on, that in the atmospheric ocean surrounding the earth, there are nearly fifteen pounds of air above every square inch of the surface of the earth ; and that the air nearest the earth, and bearing this superincumbent weight or pressure, has the density of an ounce and a quarter of weight to a cubic foot of volume. We further find that such air is reduced to half its bulk, or becomes of what is called double atmospheric density, by an additional pressure of fifteen pounds on the inch, and of triple density, by tripple pressure, and so forth ; and on the other hand, that it dilates to double bulk, if the pressure be diminished to half, and to any greater bulk, even beyond a thousand-fold, if the pressure be diminished in a corresponding degree ; and any air bearing a given force or pressure, is always acting as a spring of that force on whatever it touches. It is very important to be familiar with this truth or law, for it holds very nearly with respect to all aeriform fluids as well as common air, and throws light, therefore, on the action of steam-engines, air-guns, pneumatic machines generally. It also explains the condition of our atmosphere as to density at various elevations ; telling us, for instance, that when a balloon has risen through half of the atmospherical mass, the air around it will be of only half the density which exists at the surface of the earth. We know not exactly to what extent the rarefaction of air may go on the removal of pressure ; in other words, at what distance the gravity of the particles becomes just a balance to their mutual repulsion ; and therefore we know not exactly -what the degree of rarity is at the top of our atmosphere ; but we know that it must be exceedingly great, from the fact that the air left in the receiver of an air-pump has still spring or elasticity enough to lift the valve of the pump, when less remains than the thousandth part of the original quantity. In the most perfect air-pumps, that the exhaustion may be as complete as possible, the machine itself is made to raise the valve. The expansion of air is well illustrated by a bladder, having a very little air in it, placed under the receiver of an air-pump. On exhausting the receiver, the bladder gradually swells, with force sufficient to lift a moderate weight laid upon it, and at last appears quite full, and may even be burst. A shriveled apple treated in the same way becomes,plump. The explana- tion of such* phenomena is, that at first the air in the bladder or apple is in a ELASTICITY OF AIR. 161 Fig. 87. state of condensation, like all air, at the surface of the earth under the pres- sure of the superincumbent atmosphere; but that its volume increases as that pressure is diminished by the air-pump : it is rarefied in the same propor- tion as the air which remains in the receiver surrounding it. The curious instrument called the air-guji has a strong globular vessel of copper attached under the lock, into which air is usually forced to be thirty or forty times as dense as the air in the atmosphere around : hence the pressure or elasticity tending outwards is thirty or forty times fifteen pounds on the inch, and when the valve is opened for an instant by the action of the lock, a portion of the air issues and propels the charge with this force. The effect of air thus condensed nearly equals that of gunpowder, and one charge of the ball suffices for many shots, the force, however, becoming less for every successive discharge. If a bottle or vessel a b } partly filled with water, have a tube c d passed tightly through the cork to near the bottom of the water ; and if more air be then forced through this tube in any way, so as to accumulate in the upper part of the vessel above the water surface a b; on turning the cock c, which opens the tube, the elasticity of the condensed air will press the water out as a beautiful jet, to a height pro- portioned to the condensation, and gradually diminishing as the condensation diminishes. Or if such a vessel, with air of common density, be placed under a tall air-pump receiver, on working the pump so as to diminish the density of the air in the receiver, the jet of water will equally rise. A table-lamp,, by the force of condensed air, may be supplied with oil from a reservoir far below the wick : and lately an enema syringe and a shower-bath have been constructed on the same principle. The elasticity of air is rendered very serviceable in con-- nection with great water-pumps, such as those used for the supply of cities. A pump throws its water by a distinct gush at each stroke, while the current through the pipe towards the city should be uniform. Now uniformity is attained by causing the gushes from the pump a to enter by the passage b at one side of a large vessel c, of which the. upper part is full of the condensed air, and from the other side of which at d the water issues on its way. The air in this vessel (called the air-vessel) is condensed, as a spring, by the entering water, and its resisting elasticity, both immediately, and afterwards during the interval of the strokes, forces the water along the pipe d. Each entering gush has only the effect of compressing the air a little more for the time, while the flow in the great pipe continues nearly uniform. The pump itself is made to take in a little air at each stroke, so that not only is the vessel always sup- plied, but some air is constantly passing on with the water, and effecting the highly useful purpose of giving an elasticity to the whole contents of the pipe and its ramifications. The same object is attained by the same means in the fire-engine used to check conflagration. In it there are generally several water-pumps working 11 Fig. 88. 162 PNEUMATICS. together, which throw their interrupted supply into an air-vessel whence it passes in a nearly uniform jet to the point desired. The compressibility and corresponding spring of air are remarkably exhi- bited in that singular contrivance of modern times, the diving-bell, in which men now descend with safety to, considerable depths in the ocean, there to reside and labor, attaining many objects of high importance to them : they recover sunken treasures, they are enabled to pursue works of submarine architecture, as in constructing light-houses and noble harbours, where formerly no foundations could have been laid, &c. The diving-bell, in point of utility, has proved a remarkable contrast to its sister invention, the balloon, which, although so wondrously bearing man aloft to the regions of the clouds, has brought him as yet little advantage to compensate for the many fatal accidents which its use has occasioned. The diving-bell is a large heavy open-mouthed vessel, with accommoda- tion in it for one or more persons. It is let down into the water with its mouth undermost, from a crane to which it is suspended, and which rests .on a suitable carriage either on the shore, or on the deck of a ship, or barge fitted for its service. On first entering the water it appears full of air; but air being compressible, according to the law now explained, and the pressure of the water around the descending bell increasing with the depth, the volume of the air gradually diminishes, and at thirty-four feet is reduced to half. The bell, then, unless more air be supplied, will of course be half full of water, and a person breathing in it, at each inspiration will receive twice as much air into the lungs as when breathing at the surface. A constant supply of fresh air is sent down to the bell by a forcing-pump above : and the heated and contaminated air, which has served for respiration, and which rises to the top of the bell, is allowed to escape by a cock placed there for the pur- pose. The men who work at a distance from the bell have tubes of com- munication with it, by which they inhale the air required ; and they allow the used air to rise through the water above them. A man cannot breathe comfortably by such a tube if he be either much above or much below the level of the water in the bell ; for if above, the air in the bell is more com- pressed than his chest, and is forced towards him so as to require an effort to control its admission; and if below, his chest is bearing greater pres- sure than the air in the bell, and he must therefore act strongly with the muscles of the ribs to draw the air down to him. A phenomenon similar to this takes place when two bladders of air are connected by a long tube, and immersed in water to unequal depths, the air being always strongly forced from the lower into the upper one, because the lower one is more pressed. The difficulty of pumping air down to the diving-bell increases, of course, with the depth to which it has ascended : for if the bell be so low that the water is pressing on the air in it with a force of fifteen pounds per inch, ( which would happen at thirty-four feet, ) it is evident that a syringe or pump can not inject more air unless it act with a force greater than this. Divers might often, if not always, more conveniently receive their supply of air through tubes from an air vessel kept charged to the necessary density in a boat over them, or on the shore, than from a bell below. If they would, moreover, dress in India-rubber cloth, and use a hood of metal with windows for the head, they might work under water without wetting any part but their hands. It is remarkable, when the use of the diving-bell has become so familiar, that a kindred and still more simple contrivance of the same class has not been introduced for certain purposes, particularly of sudden emergency, such ELASTICITY OP AIR. 163 as to aid in the recovery of the bodies of drowning persons. A ten-gallon cask, or vessel of any kind, filled with air, and made heavy enough just to sink in water, with a breathing tube from it like that of a diving-bell, would be a provision of air for a man below water for ten minutes ; and a man with it under his arm, might instantly descend from a boat or walk from the shore, into water of any depth, to recover the body of a fellow-creature lately sunk, and in time probably to save the life, which a few minutes wasted in waiting or in unsuccessful dragging would suffer to be lost. The author would pro- pose this as an addition to the apparatus of the Humane Society for the recovery of persons apparently drowned. It shows the remoteness from common trains of thinking of the truths connected with the constitution of our atmosphere and sea, when a means so simple and easily procured should never have been thought of or tried in any way by pearl-fishers, or by per- sons who gain their bread by diving to recover things dropped overboard in harbours or anchoring stations ; all of whom have hitherto been limited to the single gulp of air taken on descending. In the case of a man working under water, cask after cask of air might be sent down, to enable him to remain as long as necessary. There is an exceedingly beautiful philosophical toy, of which the action depends chiefly on the elasticity of air ; and as it moreover illustrates most of the laws of fluidity, it is deemed worthy of Fig. 89. description here. It is a small balloon or thin globe of glass c, having an opening at the bottom, and its little car or basket hanging to it. If put to float in water while the globe con- tains air only, it is so light that half the globe remains above the surface ; but water may be introduced to adjust the specific gravity of the whole, until it becomes only a little less than that of water. If the balloon be then placed in a tall jar of water a b, the moutn of which is closely covered by bladder- skin or India-rubber tied upon it, on pressing such covering with the hand, the balloon will immediately descend in the water, to rise again when the pressure ceases, and will float about, rising, or falling, or standing still, according to the pressure made. The reason of this is, that pressure on the top of the jar first condenses the air between the cover and the water surface ; this pondensation then presses upon the water below, and by influencing it through its whole extent, compresses also the air in the balloon globe, forcing as much "to ore water into this as to render the balloon heavier than water, and therefore heavy enough to sink. As soon as the pressure ceases, the elasticity of the air in the balloon repels the lately entered water, and the machine, becoming as before, lighter than water, ascends to the top. If the balloon be adjusted to have a specific gravity too nearly that of water, it will not rise of itself after once reaching the bottom, because the pressure of the water then above it will perpetuate the condensation of the air which caused it to descend. It may even then, however, be made to rise again by inclining the water-jar to one side, so that the perpendicular height of water over it shall be diminished. This toy proves many things the materiality of air r by the pressure of the hand on the top being communicated to the water below through the air in the upper part of the j-ar the compressibility of air, by what happens in the globe just before it descends the elastic force of air shown in expansion, when, on the pressure ceasing, the water is again expelled from the globe the lightness of air ; in the buoyancy of the globe : -it shows, also, that in a 164 PNEUMATICS. Fig. 90. fluid the pressure is in all directions, because the effects happen in whatever position the jar be held it shows that pressure is as the depth, because less pressure of the hand is required the farther that the globe has descended in the water and it exemplifies many circumstances of fluid support. A young person, therefore, familiar with this toy, has learned the leading truths of hydrostatics and pneumatics, and has had much amusement as well as instruction. On the same principle as the balloon now described, three or four little figures of men may be formed of glass, hollow within, and having each a minute open- ing at the heel, by which water may pass in or out. If these be placed in a jar as the balloon was, and be adjusted by the quantity of water admitted into them, so that in specific gravity, they shall differ a little from each other, and if then, a gradually increased pressure be made on the cover of the jar, the heaviest figure will descend first, and the others will follow in suc- cession , and they will stop or return to the surface in reverse order when the pressure ceases. A person while exhibiting these figures to spectators who do not understand them, may appear only carelessly to rest his hand on the cover of the jar while he is making the required pressure, and he will seem to have the power of ordering their movements by his will. If the jar containing the figures be inverted, and the cover be placed over a hole in the table, through which, unob- served, the exhibitor can act by a rod rising through the hole and obeying his foot, he may produce the most amusing and surprising evolutions among the little men, in perfect obedience to his word of command. The beautiful fountain, called the fountain of Hiero, by which water is made to spout far above its source, depends for its action upon the resisting elasticity of compressed air. The vessel d is first filled with water, while b and a contain air only. On then pouring water into a, the water of d darts upwards through the jet-pipe e,to an elevation nearly equal to the length of the tube from a to b. The reason is, that the water from a descends by the tube to b, and compresses the air at c ; which compression conveyed along the other tube from c to 5, acts on the water in the vessel r/, and causes it to jet. As the pressure is produced by the column of water a b, the jet is proportioned to the length of that column. This kind of fountain may have its parts concealed under a variety of forms as here exemplified, and may thus become a beautiful ornament among flowers in a sum- mer drawing-room. It may be made of size to play for an hour or more, and it will always recommence on the water being shifted from the low to the high reservoir. The useful table-lamp, consisting of a simple column or pillar with the oil rising to the flame from far below, is a Hiero's fountain, only the Fig. 91. PRESSURE AS THE DEPTH. 165 oil, instead of being allowed to jet out, rises in a tube to the flame. The contrivance for maintaining the two columns always of the same length, not- withstanding the expenditure of oil has to be explained some pages hence. Having now explained the two peculiarities which distinguish aeriform from other fluids, viz., their lightness and extensive elasticity, we proceed to show that they have the four other properties already described under hydrostatics, as belonging to fluids generally : and first, " Pressure in all directions." ( Read the Analysis, at pages 140 and 172.) A quantity of air or gas shut up in any vessel and compressed, is equally affected throughout, and its tendency to escape from the pressure is equal ill all directions, as is proved by the force necessary to keep similar valves close wherever placed. Hence the hydrostatic press and hydrostatic bellows described in the last section, which depend for their action on this law, may be worked by air or gas as by a liquid. Owing to this law, air, when allowed, will always rush from where there is more pressure to where there is less. The actions of the common fire- bellows, and of the animal chest in breathing, blowing, sucking, &c., are so many instances. The suddenness with which any compression made on part of a confined aeriform fluid is communicated through the whole, is strikingly seen in the simultaneous increase or burst of all the gas-lights over an extensive build- ing or even in a long street, at any instant when the force supplying the gaa is augmented. Many very interesting illustrations of the fluid pressure of air being in, all directions, will occur under the next head, joined with proofs of the atmospheric pressure being as the depth. "Pressure as the depth" On first approaching this subject, a person is naturally surprised to hear the depth or height of the atmosphere spoken of as something perfectly ascertained, although nobody can ever have approached the surface to mea- sure it ; but science often furnishes means of reaching precise truth, in. cases where ignorance would not' even dream of the possibility of making an approximation. It may facilitate the apprehension of this point as regards air, to describe first some parallel cases in which water is concerned. The bottom of a lake evidently supports all the water in the lake, and each portion bears just the weight of the water directly over it : a means then of ascertaining the weight or pressure of water on any portion of the bottom would tell how much water stood over that portion, and by the known rej^,tion of the weight and bulk of water would tell also the depth at that part. In like manner the ocean of air which surrounds the globe rests with its whole weight upon the surface of the globe, and each portion of the surface bears its share : if we ascertain, then, the pressure of the atmosphere on a given extent of the surface, we find how much air is stand- ing directly over it; in other words, the weight of a column of air resting on such surface as its base, and reaching to the top of the atmosphere. Having then the weight of the whole column, and finding the weight of a given bulk of it at the botton (ascertained as described at page 158,) and knowing the law of aerial elasticity (explained at page 158, ) we determine the depth or height of the column by a simple calculation. Now accurate 166 PNEtJM ATICS. experiments show that there are nearly fifteen pounds of air over every square inch of the earth's surface ; producing the same pressure as would be made by a depth of water of thirty-four feet, or by a depth of quicksilver of thirty inches ; and from this fact and the ascertained lightness and elasti- city of air, we know that its depth on earth must be nearly fifty miles, which, as already stated, is about as much in relation to the size of the garth as the tenth of an inch is to a globe of one foot in diameter. The remaining part of this section has chiefly to trace the effects of this mass of matter resting upon the earth's surface, and as a fluid embracing and compressing every object placed there. Water is a substance much more obvious to the human senses than air, and which is constantly under observation ; yet many of its most important agencies escape the notice of common observers. Few persons, for instance, of themselves discover the law explained in the last section, of the pressure in water being proportioned to the depth : but when made to observe that a piece of cork plunged deep into it is compressed to much smaller bulk, and that strong empty vessel of glass, or even of metal under the same circum- stances, are crushed or broken inwards, and that pieces of sunken wood are, at great depths, filled with water through all their pores, so as to become nearly as heavy as stone, &c., their minds are roused to a sense of the import- ant fact that a fluid presses, and in proportion to its depth. If the truths of hydrostatics thus escape notice, we need not wonder that those of pneu- matics escape still longer. If a piece of bladder-skin or a pane of glass be laid at the bottom of a vessel, holding water, the bladder or glass exhibits no sign of being pressed upon, although it bears on its upper side the whole weight of the water directly above it: the reason being that water beneath the bladder resists just as strongly as the water above presses, in the same way that one stone in a pillar resists those above it : but if the bladder be tied closely over the mouth of a common drinking glass or tumbler filled with water, and placed at the bottom of the vessel, and if then, by means of a syringe or pump, the water be extracted from within the glass, the bladder itself has to bear the whole pressure of the water above it, ( independently of a pressure of air, to be explained afterwards, ) and will probably be torn or burst. The degree of pressure, and consequently the depth of the water, in such a case, might be ascertained by placing some support, of which the action could be measured, under the bladder to sustain it after the removal of the interior water. Now this case may be closely copied in our atmosphere or sea of air. A glass held in the hand is immersed in the fluid air, and is full of it as the other glass was supposed full of water : its mouth may be covered over with bladder, and no external pressure will be apparent, because there is a resistance of the air within, just equal to the pressure of the air on the outside : but if the air be extracted from under the covering bj^rneans of an air pump, the bladder is first seen sinking down and becoming hollow from the weight of the air over it, and at last bursting inwards with a great noise or crack. By placing a circular piece of wood under the bladder-skin, for it to rest on, and a spring of known force to support the wood, we may ascertain very nearly the weight and pressure of the air over it. This mode, however, of ascertaining the weight of the atmosphere, is not that commonly used, but is described here as a good illustration of the present subject; the problem being solved much more elegantly and accurately by means of the barometer described farther on. The phenomenon of atmos- pheric pressure is often exhibited by placing the hand on the mouth of a ATMOSPHERIC PRESSURE ON SOLIDS. 167 glass so as to. cover it closely, and then extracting the air from underneath the hand : the weight of the atmosphere holds the hand down on the mouth of the glass with the force of fifteen pounds to the inch. As should follow, from the pressure of fifteen pounds per inch thus detected at the surface of the earth, being the weight of our superincubent atmo- sphere, we find that exactly as we rise from the earth, and leave part of the atmosphere beneath us, the pressure diminishes. This fact now furnishes the readiest means of ascertaining the heights of mountains and of balloon ascents, as will be explained in considering the barometer. After the many explanations here given of fluid pressure being equal in all directions, it is almost superfluous to remark, that the downward weight of the atmosphere becomes a pressure in all directions. This is seen in the fact of the bladder seen above, being as readily burst if turned sideways as if turned directly upwards. Every body or substance, therefore, on the surface of the earth, dead or living, solid or fluid, is compressed with this force. In general the pressure on one side of a body, is just balanced by the equal pressure on the other, so that no sensible effect follows; and it is on this account that philosophers were so long in discovering it at all, and that half-informed persons are still disposed to doubt its existence ; but the proofs offered on all sides to the now awakened attention are irresistible. We shall speak first of " Atmospheric pressure on solids." The atmosphere, then, presses on the two sides of a plate of glass or metal, with force of fifteen pounds on the inch. Under ordinary circumstances, no sensible effect follows, because the opposite pressures counterbalance ; but if two plates of smooth glass or metal be laid against each other, and the air be prevented from entering between them, they cannot be separated by less force than fifteen pounds per inch of their surface. In like manner, to draw down the piston of a syringe from the bottom of its barrel, while no air is allowed to enter between them, requires force of fifteen pounds to the square inch of surface of the piston. But if the experiment be made in the exhausted receiver of an air-pump, the piston falls by its own weight. It is pushed back immediately on re-admitting the air. Wherever a vacuum is produced at the surface of the earth, there is an external pressure, of the force stated, seeking admittance all round. An air-pump receiver of five inches diameter has nearly twenty square inches of surface in its upper part or roof, and bears a weight or pressure of atmosphere, of twenty times fifteen, or three hundred pounds. W T hile it has air within it, this pressure is exactly balanced, and is not sensible ; but when exhausted on the plate of the air-pump, it is pressed against the plate with this force. As the atmospheric pressure is in all directions, the pump-plate, of course, is equally pressed upwards against the receiver, and the sides of the receiver are pressed towards each other. This explains why air-pump receivers must be made arched or of dome-shape to withstand the great pressure. A flat piece of glass of great thickness, laid upon the upper mouth of a receiver, so as to form an air-tight cover to it, is broken instantly by exhausting the air beneath ; and a bottle or receiver with flat side, when exhausted suffers in the same manner. Illustrative of this pressure on solids there is the experiment of the Magde- burgh hemispheres, as it is called. Two hollow half globes of metal a and 168 PNEUMATICS. the world. b, are fitted to each other, so that their lips wjien touching may be air-tight. While there is air between them or within, resisting the pressure of the outward air, they can be separated from each other without difficulty ; but when the air is exhausted from within by the air-pump, a force is required to separate them of as many times fifteen pounds as there are square inches in the area of the mouth. The air is extracted by unscrewing one of the handles at b, and then connecting the remaining stalk (which is hollow and has a stop-cock) with the air-pump. This experiment merits recollection, because it was one of the first which drew attention to the material nature and properties of the air; and it astonished Otto Guericke, Burgomaster of Magdeburgh, the inventor, had hemispheres made of three feet in diameter, and once when he exhausted them, on the occasion of a public exhibition, twenty coach-horses of the emperor were unable to pull them asunder. There being no air-pump when Guericke began his experiments, although he himself invented it afterwards, he originally emptied the balls of their air by first filling them with water, and then extracting the water by a common pump or syringe applied to the bottom. It is a phenomenon of the same kind as the last described, when a boy with his foot presses a circular piece of wet leather as a, against a flat-faced stone as b, and then lifts the stone by pulling at a cord c, rising from the centre of the leather. , If the leather be so close in its texture that air cannot pass through it, and stiff enough not to be puckered or drawn together, he must exert a force before detaching it, of as many times fifteen pounds as there are square inches of surface covered by it for such is the weight or pressure of the air over it, while there is no counterbalancing pressure underneath nearer than on the other side of the stone. The weight of the stone that may be lifted is thus determined by the size of the leather. The contrivance has been called a sucker, or pneumatic tractor. A very large sucker applie 1 upon a rock or wall, would resist the pull of horses like the Magdeburgh hemispheres. This contrivance seems suited to some purposes of surgery. It might assist, for instance, in raising de- pressed portions of a fractured skull, and might thus sometimes save the operation of trepanning : for such a purpose it would be preferable to the small cupping- glass sometimes used, from its being perfectly inactive, except during the instants when pulled at; whereas the cupping-glass, by keeping up a continual flow of blood to the part, might do injury. There is another surgical application spoken of in the last section of the present part, which the professional reader may consult immediately. It is from having feet that act on the principle of the tractor, that the common fly and other insects can move along ceilings, and even polished surfaces of glass or metal with their bodies hanging downwards ; and there are many marine animals which attach themselves to rocks, or other objects by a similar action. If two pneumatic tractors be applied to each other, men pulling opposite ways, to separate them, must act with a force of fifteen pounds to the square Fig. 93. ATMOSPHERIC PRESSURE ON LIQUIDS. 169 inch of the surface of contact, as if they were separating the Madgeburgh hemisphere. The case of the pneumatic tractor may be well illustrated by an experi- ment made in a vessel containing a liquid. If a body with a flat surface be applied to the bottom of the vessel so as perfectly to exclude the liquid, the body bears the whole weight of liquid directly over it, and cannot be detached without force equal to this.. The case is striking when a flat piece of cork is pushed against the smooth bottom or side of a vessel containing mercury, and is found not to rise again when the hand is withdrawn from it, but to be firmly held down by the weight of the mercury. We have to remark that in such experiments made in vessels open to the air, the weight of the atmosphere on the liquids adds a pressure of fifteen pounds on every inch of the surface of a body immersed in it. " Atmospheric pressure on liquids" The pressure of the atmosphere on liquids produces many important effects, and now that we comprehend them, we wonder that they should have been so long misunderstood. We have familiar examples of it in the work- ing of pumps and syphons. All such phenomena, in former times, were referred to what was called nature's horror of a vacuum, or to an obscurely imagined principle of suction. It was not until the time of Galileo that their true nature began to be detected. The discovery has led to many very important results in the arts. Persons may at first have a difficulty in conceiving that a fluid so rare and subtle as air should affect or resist u dense liquid like water : but the action or resistance of air in contact with water, is familiarly shown in the facts that a glass does not become full of water when plunged, with its open mouth downwards, from the air into water; and that when a tube, open at bol^i ends, has been partially immersed in water, and, therefore, partially filled, the water can be forced out of it by blowing air in at the upper end, to return only when the blowing ceases. Then it may be recollected that a hundred pounds of feathers are as great a load as a hundred pounds of lead. That there are fifteen pounds of air above every square inch of the earth's surface, is confirmed by the effects above described of the atmospheric pres- sure on solids; and we now proceed to show that many of the phenomena among liquids, which long appeared so mysterious, are merely the necessary consequences of the same pressure upon them. It will facilitate the com- prehension of these effects, if we first view them as they may be produced by more visible agents, viz., by one liquid pressing upon another ; and for this purpose the author has contrived the apparatus represented in the next page, in which a layer of oil rests upon a layer of water, or upon a layer of- mercury. It has already been shown, that an ocean of oil, spread over the earth, to have the same weight as our atmosphere, requires to be about thirty-seven feet .deep A vessel, then, a b c, with water in it up to the level W, and with thirty-seven feet of oil above this, up to the level 0, is fitted to illus- trate many of the phenomena of atmospheric pressure on liquids. The following are the seven principal cases. 1st. The weight of the oil pressing with a force of fifteen Ibs. per inch on the water at W, would not at all disturb the level surface of the water. Neither does the weight of the atmosphere o*f fifteen Ibs. per inch disturb any liquid surface. 170 PNE UN ATICS . Fig. 94. 2. If the oil were gradually poured into the vessel a b c, over the water, the water would rise in the tube i w, as already ex- plained by the figure at page 143 ; so that when there were thirty-seven feet in height, or fifteen pounds in weight of oil on the inch, the water i w would stand thirty-four feet above its level in the large vessel. If these thirty-four feet of water were then lifted out of the tube by a plug or piston drawn up from the bottom of it at i, a second equal quantity would be pressed up by the oil, to be removed, if desired, in the same way as the first, and the tube and piston would constitute a pump. Now when the atmosphere, instead of the oil, is allowed to press upon a water surface in such a vessel, but is excluded from the tube, the water rises in the tube thirty-four feet, as in the last case } and if this quantity be lift- ed out of the tube by a piston, a second equal quantity is pressed up, and the tube and piston become a complete example of the common lifting or sucking pump. We have to describe it more particularly hereafter. 3d. If there were a quantity of mercury or of quicksilver at the bottom of the vessel ale, filling it up to the level M, and if a tube i m issued from under this level, the mercury pressed upon by thirty-seven feet of oil would r\se in this short tube as the water did in the larger j but by reason of its greater specific gravity, it would only reach a height of thirty inches above its level, the water having stood at thirty-four feet. Now thirty inches of mercury is the height of column which the atmospheric pressure, acting in the same way really produces, as is seen in a similar apparatus made expressly for measuring that pressure, and called a barometer or measure ' of weight. 4th. If a tube d, of an inch square and open at both ends, were plunged into the. oil, it would of course always be full up to the level of the oil on the outside of it ; and if it were pushed low enough to touch the water at W, it would just contain fifteen pounds of oil resting on an inch square of the water-surface at its mouth j which surface would therefore be bearing a weight of fifteen pounds like every inch of the surface around, but would not yield, owing to the force with which it tended upwards to escape from the pressure corresponding to its depth in the oil. Then if the tube were pushed a little farther down, and if, by a piston or plug in it, the fifteen pounds of oil were lifted out of it, water would rise into it until enough had entered to reproduce the pressure of fifteen pounds on the surface below as before ; that is to say, the water would rise thirty-four feet, as in the external tube w i. This internal tube and piston again would form &pump. In like manner, when a tube open at both ends is plunged from the air into water, the air presses on the surface of the water within the tube, as on the surface around it, with a force of fifteen pounds to the inch, and the two surfaces are not affected by the* equal pressures ; but if, by a piston, we lift the air out of the tube, as we suppose the oil lifted in the last experiment, ATMOSPHERIC PRESSURE Off LIQUIDS. 171 the water will then rise, following the piston to the altitude of thirty-four feet. This arrangement of parts is the most usual for the lifting or house- holt pump. 5th. If a common bottle or vessel of any shape, as the bent tube e, were filled with water, and placed under the oil with its mouth or mouths reach- ing below the water surface at the level W, it would remain full of water, owing to the pressure of the oil surrounding it. For a similar reason, any such vessel or tube, surrounded only by air, when filled with water, and placed with its mouth or mouths under the surface of water, remains full ; and if such a bent tube has one of its ends in another vessel lower than the first, a current is established in it; the contrivance being then called a syphon. 6th. A fish in the water below the level W, would be bearing the pres- sure of the oil from to W, as well as the pressure of the water. So a fish in water open to the air, is bearing the atmospheric pressure of fifteen pounds per inch, in addition to that of the water itself. This is proved by extracting the air from over water in which a fish is swimming : for then the air-bag of the fish, situated near its under side, as already described, immediately dilates and turns the fish upon its back. x 7th. To separate the Magdeburgh hemispheres, or to produce a vacuum in any way, under the water level W, would require force proportionate to the weight of oil above, in addition to that required on account of the water ; and to separate the Magdeburgh hemispheres under any water- surface pressed upon by the atmosphere, a force is required of fifteen pounds per inch beyond what would balance the effect of the water itself. Fig. The following remarks illustrate more minutely some of the objects which we have just been explaining. The common lifting-pump (or sucking-pump as it used to be called,) is then merely a barrel a b, with a close-fitting moveable plug or piston in it c. When the lower end b } is plunged into water, and the piston is drawn up from the bottom, the atmosphere being prevented from pres- sing on the surface of the water within the tube, the pressure on the surface external to the tube, drives the water up after the piston. That the water which thus rises ma^y not fall again, there is a valve or flap at the lower part of the pump-barrel b, which opens only to water passing upwards ; and* that the piston may be allowed to pass downwards through the water in the barrel, to repeat its stroke, there is in it a similar valve. The piston, in rising during a second or succeeding stroke, causes all the water above it to run over at the spout d. Formerly a lifting-pump was said to act by sucking the water up from the well beneath it ; the true meaning of which phrase we now perceive to be, that the piston merely lifts or holds off the air which was pressing on the water within the barrel, and allows the water to rise in their obedience to the external pressure of the air around. The reason is apparent, then, why, in the lifting pump, the water will only follow the piston to a certain elevation, viz., until its weight balances the external pressure of the atmosphere. 172 PNEUMATICS. Fig. 96. When the piston of a pump is solid, or without a valve, as at c, the machine is called a forcing-pump. The water rises beneath the piston, as already ex- plained for the lifting-pump, but then as it cantiot pass through the descending piston, as in the lifting- pump, it is forced into any other desired direction, as to d. A forcing-pump can bring water from only thirty-four feet below the piston, but can send it to any elevation. In forcing-pumps, it is usual to make the water enter an air-vessel d a (already explained at page 161,) from which it is again urged by the elastic air, through the pipe &, in a, nearly uniform stream. The animal action of sucking is an approximation to what we have described in the lifting-pump. The difference is that the chest or mouth can make only a partial vacuum, and therefore cannot raise a liquid very far. A syphon remains full of liquid, although partially raised above the general surface of the liquid, as explained above. For com- mon purposes, a syphon is made of the form here represented, viz., a bent tube c b a, with one end longer than the other. To use it, the end c is first immersed in liquid, and the end a being then stopped for the time by the finger or a cock, the air is extracted by the mouth or otherwise, through the small tube a d, and the atmosphere immediately fills the whole tube with liquid from c. If the instrument be then left to act, the liquid will run from the longer leg, because a long column of liquid overbalances a short one, until the shorter has drunk up all within its reach. Whether the external extremity be in the air only, or immersed in liquid, makes no difference, except that the immersion shortens so much the de- scending column. If both extremities be immersed in liquid, and in different vessels, by alternately lifting one vessel or the other, the liquid will be made to pass and repass, and will come to rest in the syphon only when the surfaces in the two vessels are at the same level. Thus the same leg becomes alternately the long and the short leg, according to the height of the liquid in which it is immersed. A syphon is sometimes made with both legs equal and turned up, as here represented, so that it remains full of liquid although lifted away from the vessel, and therefore is always ready for action. As it is the same cause which lifts the water in a pump and in a syphon, the top of a syphon must evidently be within thirty-two feet of the water-surface below. In the syphon as the cases of balancing liquids, described at page 131 (which see,) the comparative diameters of the legs are of no importance, nor their oblique length, provided the perpendicular heights of the two columns have the neces- sary relation : even an inverted tea-pot may be used as a syphon. This truth is well exemplified in what may be called the syphon-paradox an exact PRESSURE OF LIQUIDS. SYPHON. 173 Fig. 98. counterpart of the paradox of the " Hydrostatic Bellows," already explained. If the apparatus of the bellows be filled with water in the ordinary way (see page 130,) and be then reversed or turned so that the tube becomes like the long leg of a syphon, the little stream of water issuing from it at a will lift as great a weight suspended from the board d, as the same slender column in the standing position can lift upon the board. As farther illustrative of the atmospherical pressure exerted in producing this effect, and in rendering a syphon active, we m^r advert to the striking fact, that a long small tube of water screwed into the side or bottom of a close cask of water so as to communicate with it, and then allowed to discharge like the long leg of a syphon, will cause the cask to be crushed inwards, just as the same tube screwed into the top of the cask, as repre- sented at page 131, causes the cask to burst outwards. The syphon is very useful for drawing off liquids, where there is a sedi- ment that should not be disturbed, or where it is desirable not to make an opening in the lower part of the vessel. A large syphon would empty a lake or mill-pond over its bank without injuring the bank. To fill a large syphon that it- may act the most convenient way is, instead of pumping out the air from it, to close the two ends for the time, and to pour in water through a cock at the top. There is a pretty syphon-toy,"called a Tantalus-cup, having in it a stand- ing human figure which conceals a syphon. The short branch of the syphhon rises in one leg of the figure to reach the level of the chin, and the long branch descends in the other leg to pierce the bottom of the cup towards a reservoir below. On pouring water into the cup, the syphon begins to act as soon as the water reaches 'the chin of the figure, and the cup is then emptied as if by magic. Among the infinitely varied water-drains or courses in the bowels of the earth, some are syphons, and produce what are called intermitting wells or fountains. These may alternately run and cease for longer or shorter periods, according to the comparative magnitudes of the collecting reservoir and the' drain. The reservoir may be an internal cave of a mountain, receiving a regular supply of water by a slow filtering of moisture from above, and the drain is a syphon-formed channel, which^ like that of the Tantalus-cup, begins to act only when the water in the reservoir has reached the level of the top of the syphon, and then carries off the water faster than it is supplied. There are some fountains that flow constantly, but at regular intervals have a remarkable increase. In them a common spring is joined with a syphon-spring. The author has suggested an application of the syphon, which obviates a strong objection to the high operation for stone, as explained in the next medical section. The following facts have close relation to those now explained, as farther illustrative of atmospheric pressure on liquids. A long glass of jelly, if inverted and placed with its mouth just under the surface of warm water, will soon be found to have lost the jelly, but to be full of water in its stead. The jelly is heavier than water, and when melted by the heat sinks down, and is replaced by water from below, sent up by the atmospheric pressure. 174 PNEUMATICS. The slaves in the West Indies steal rum, by inserting the long neck of a bottle full of water through the top aperture of the rum-cask. The water falls out of the bottle into the cask, while the lighter rum ascends in its stead. The common water-glass for bird-cages has its only opening near the bot- tom through the neck b ; yet no water. can escape from it but when the level of the water at c, in the open part, becomes low enough for some air to pass into the body of the glass by the channel b. When a bubble of air does pass in, an equal bulk of water comes out, and by raising the water level in c, pre- vents the passage of more. An ink-glass made on this principle preserves the ink well, because there is so small a surface exposed to the air; if made too , . large, however, the accidental expansion of the air O ]C i n it by heat may cause it to overflow. In the common Argand or fountain-lamp, the provision of oil is in a vessel like an inverted bottle, higher than the flame, and with its mouth immersed in a small reservoir of oil, nearly on a level with the flame, then no oil can escape from above, but as the flame consumes the free oil from the' small reservoir, which supply is thus maintained always at the same elevation. In the Hiero's fountain lamp, mentioned at page 164, that the two balancing columns of oil may be always of the same height, the oil is suppplied to them from high reservoirs, with the mouths dipping in them as above described, and keeping their tops, therefore, always at the same level; and that the descending column may not be shortened by the rising of the oil in the low reservoir c. the tube containing it is turned up at the bottom like an end of the " ever ready syphon/ 7 and discharges near the top of c. We have hitherto been contemplating only the direct weight or downward pressure of the atmosphere on liquids : in the following instances we have proof of the same pressure acting upon them in all directions. If a bottle or cask be filled with liquid, and closely corked, and if a small hole be then drilled in the bottom or side, the liquid will not escape by it, because of the existing pressure of the atmosphere, and of there not being room in the opening for a current of air to enter while the current of water escapes : but if a second hole be drilled in the top, a jet from the lower opening will follow immediately, because then the air will press on the upper surface of the liquid as well as on the lower, and the weight of the liquid will be free to act : thus, a cask, of beer or wine cannot be emptied by a cock near the bottom, unless what is called a vent-hole be made at the top. If the lower opening, however, in any case be so large, that the air may enter by one side of it, as is seen in decanting a bottle of wine. In such a case, it is the interrupted entrance of the air which causes that gurgling sound so delightful to the ear of the drunkard, instead of allowing the smooth stream which fall from a funnel. Even a large opening at the bottom of a vessel which is close above, may be prevented by the pressure of the air, from discharging liquid if any mutual passing of the two currents of air and liquid be rendered difficult. An inverted bottle of water will not discharge, if a piece of paper simply be applied against its mouth. Even a wineglass filled with water may be ATMOSPHERIC PRESSURE. BAROMETER. 175 inverted, and yet will spill none, if the piece of paper, laid loosely upon its mouth, be held to it during the turning, the pressure of the atmosphere against the paper keeping it in its place, and supporting the water above it. Any vessel or tube of water of less height than thirty-four feet may be kept closed at the bottom in the same way. The animal body is made up of solids and fluids, and is affected by the atmospheric pressure accordingly. There is a difficulty at first in believing that a man's body should be bearing a pressure of fifteen pounds on every square inch of its surface, while he remains altogether insensible of it : but such is the fact, and the reason of his not feeling the fluid pressure is its being perfectly uniform all around. If a pressure of the same kind be even many times greater, such, for instance, as fishes bear in deep water, or as a man supports in the diving-bell, it equally passes unnoticed. Fishes are at their ease in a depth of water where the pressure around will instantly break or burst inwards almost the strongest empty vessel that can be sent down; and men walk on earth without dis- covering a heavy atmosphere about them, which, however, instantly crushes together the sides of a square glass bottle emptied by the air-pump, or even of a thick iron boiler, left for a moment by any accident, without the coun- teracting internal support of steam or air. The fluid pressure on animal bodies, thus unperceived under ordinary cir- cumstances, may be rendered instantly sensible by a little artificial arrange- ment. In water, an open tube partialy immersed becomes full to the level of the water around it, and the water contained in it is supported, as already explained, by that which is immediately below its mouth : now a flat fish resting closely against the mouth of the tube, would evidently be bearing on its back the whole of this weight, perhaps one hundred pounds; but the fish would not thereby be pushed away, nor would it even feel its burden, because the upward pressure of the water immediately under it would just counter- balance the weight, while the lateral pressure around would prevent any crushing effect of the upward and downward forces. But if, while the fish continued in the situation supposed, the hundred pounds of water were sud- denly lifted from off its back by a piston in the tube, the opposite upward pressure of one hundred pounds would at once crush its body into the tube. At a less depth, or with a smaller tube, the effect might not be fatal, but there would be a bulging or swelling of the substance of the fish into the mouth of the tube. In air and on the human body a perfectly analogous case is exhibited. A man without pain or any peculiar sensation, applies his hand closely to the mouth or opening of a tube, or of any vessel contain- ing air, but the instant that the air is withdrawn from within the tube or vessel, the then unresisted pressure of the external air fixes the hand upon the opening, causes the flesh to swell or bulge into it, and makes the blood ooze from any crack or puncture in the skin. These last lines describe closely the surgical operation of cupping ; the essential circumstances of which are, the application of a cup or glass, with a smooth blunt lip, to the skin of any part of the body, and the extraction by a syringe, or other means, of a portion of the air from within the cup. To some minds the exact comprehension of this phenomenon may be facilitated, by considering the case of a small bladder or bag of India-rubber full of any fluid and pressed between the hands on every part of its surface except one : at that one part it would swell, and even burst if the pressure were strong enough. So in cupping, the whole body, except the surface under the cup, 176 PNEUMATICS. is squeezed by the atmosphere, with a force of fifteen pounds to the square inch, while in that one situation the pressure is diminished according to the degree of exhaustion in the cup, and the blood consequently accumulates there. The application of a cup with exhaustion only, constitutes the opera- tion called dry-cupping. To obtain blood, the cup is removed and the tumid part is cut into by the simultaneous stroke of a number of united lancets : and the cup is then applied again as before and exhausted, so that the blood may rush forth under the diminished pressure. The partial vacuum in the cup may be produced either by the action of a syringe, or by burning a little spirit in the cup and applying it while the momentary dilation effected by the heat has driven out the greater part of the air. The human mouth applied upon any part becomes a small cupping apparatus, and formerly, in cases of poisoned wounds, was used as such. Our present perfect cupping glasses, of stronger and more permanent opera- tion, are not yet always used, as they might be, to assist in removing the poison after the bites of rabid or venomous animals. The author has suggested an extension and modification of the operation of the dry cupping, which he believes will prove an important remedy in the hands of the medical practitioner. It is intended as a substitute for bleeding in certain cases where blood can ill be spared, and as a more sudden and effectual check than even bleeding itself, in certain cases of inflammatory disease. It is explained in the next medical section of this work. The atmospheric pressure on living bodies produces an effect which is rarely thought of, although of much importance, viz., keeping all the parts about the joints, firmly together, by an action similar to that exerted on the Magdeburgh hemispheres. The broad surfaces of bone forming the knee- joint, for instance, even if not held together by ligaments, could not, while the capsule surrounding the joint remained air-tight, be separated by a force of less than about a hundred pounds ; but on air being admitted to the articular cavity, the bones at once fall to a certain distance apart. In the loose joint of the shoulder, this support is of great consequence. When the shoulder or other joint is dislocated, there is no empty space left, as might be supposed, but the soft parts around are pressed in to fill up the natural place of the bone. When a thigh bone is dislocated, the deep socket called thee actabulum instantly becomes like a cupping- glass,* and is filled partly with fluid and partly with the soft solids. In all joints, it is the atmospheric pressure which keeps the bones in such steady contact, that they work smoothly and without noise. The barometer we have seen at page 170, is a column of fluid supported in a tube by the pressure of the atmosphere, and therefore indicating most exactly the degree of that pressure. It is an instrument now of such import- ance, both in a scientific point of view and in the business of common life, that for the sake of minds which conceive such subjects with difficulty we shall add here the two following farther illustrations of its nature. If mercury be poured into a bent tube open at both ends, it will stand at the same level in the two legs, as at a and 6, and the air will be pressing on the two surfaces at a and b with equal force of 15 Ibs. per square inch. If the air be then removed from one leg a, by a piston or otherwise, while it continues to press in the other leg b } the mercury will be pushed down in b, until the growing height of a column in a produces a weight so much greater than that in 6, as just to counteract the pressure : now this balance takes place, in fact, when the mercury in a stands about thirty inches higher than in b; that being the height of a column of mercury weighing 15 Ibs on the square inch. ATMOSPHERIC PRESSURE. BAROMETERS. 177 Fig. 100. cl If the top of the tube a were then closed permanently, the mer- cury would for ever remain elevated in it, marking most perfectly the atmospheric pressure; now this construction, only with the empty and useless part of the tube above d cut off or wanting, forms a common barometer. The exact altitude of the mercury in it is known by observing how much the surface near c is higher than that near d. Often, in such a barometer, a little mass of metal is placed to float on the mercurial surface at d, and as it rises and falls, is caused, by a thread passing from it over a wheel or pulley, to move an index like the hand of a clock con- nected with the wheel, and this index tells the degree of eleva- tion. This modification is called the wheel barometer. Again, as water at a, in the bottom of a closed pump-barrel, if pressed upon by the piston b c, of which the rod d were hollow or tubular, would rise in the rod to a height proportioned to the pressure made by the piston, so, in a straight exhausted barometer-tube, which is as this hollow piston-rod, the mercury or water rises, because the atmospheric pres- sure around it is as the piston forcing the fluid up. To make a barometer of this kind it is only necessary to procure a glass tube more than thirty inches long, and close at one end, and then having filled it with mercury, to plunge its mouth (stopped by the finger while turning) into a small cup or basin of mercury; the fluid falls away a little from the top of t]ie tube, leaving a vacuum there, and stands at the elevation which the atmospheric pressure is fitted to maintain. We know from the law of hydrostatics already explained that it is of no importance, in such a case, what the shape, or inclination, or size of the tube may be, as only the perpendicular height can measure or be measured by the pressure. This fact enables us to construct barometers with the upper part of the tube bent obliquely, PO that for one inch rise of mercury in a perpendicular tube, there shall be an advance of several inches in the oblique top, rendering any change of elevation so much more apparent. G-alileo had found that water would rise under the piston of a pump to a height only of about thirty-four feet. His pupil Torricelli, conceiving the happy thought, that the weight of the atmosphere might be the cause of the ascent, concluded that mercury, which is about thirteen times heavier than water, should only rise under the same influence to a thirteenth of the eleva- tion ; he tried and found that this was so, and the mercurial barometer was invented. Pascal then, to afford farther evidence that the weight of the atmosphere was the cause of the phenomena, carried the tube of mercury to the tops of buildings and of mountains, and found that it fell always in exact proportion to the portion of the atmosphere left below it; and he found that water-pumps in different situations varied as to sucking power, according to the same law. It was soon afterwards discovered, by careful observation of the mercurial barometer, that even when remaining in -the same place, it did not always stand at the same elevation ; in other words, that the weight of the atmosphere over any particular part of the earth was constantly fluctuating ; a truth which without the barometer could never have been suspected. The observation of the instrument being carried still farther, it was found, that in serene dry weather the mercury generally stood high, and that before and during storms Fig. 101. out sixteen hundred pounds^ and the same quantity of hydrogen gas, of easily obtained purity, weighs only one-eighth as much as two hundred pounds. Such a globe, therefore, being buoyed up, or supported in common air, with a force of sixteen hundred pounds, while, if filled with hydrogen, it only weighs two hundred, will carry up into the sky founteen hundred pounds of material and load. The first balloon was exhibited by a man ignorant of what he was really effecting. Seeing the clouds float high in the atmosphere, he thought thac if he could make a cloud and enclose it in a bag, it might rise and carry him with it. Then, erroneously deeming smoke and a cloud the same, he made a fire of green wood, wool, &c., and placed a great bag over it with the mouth downwards to receive the smoke. He soon had the joy to see the bag full, and, when set free, ascending ; but he understood not that the cause was the hot and dilated air within, which, being lighter than the sur- rounding air was buoyed up; while the visible parts of the smoke, which chiefly engaged his attention, was really heavier than the air, and was an impediment to his wishes. This modification called the hot air or fire balloon, was afterwards better understood, and was used by aeronauts, until the more commodious and less dangerous modification, called the inflammable air balloon, or balloon of hydrogen gas, was substituted. Since the modern introduction of gas lights, the carburretted hydrogen prepared for them is generally employed for filling balloons. It is con- siderably heavier than pure hydrogen, but is so much more readily obtained, that aeronauts like better to make a larger balloon to suit it, than a smaller one which obliges them to prepare the other. A thin paper bag, filled with the hot air rising from a large lamp, is a miniature hot air or fire balloon; and a common soap bubble, filled with hydrogen is a little inflammable air balloon, which mounts with great rapidity. There are, perhaps, few occasions on which a youth is more surprised and delighted than when he first beholds a balloon sailing high in the bosom of the air and bearing a human being to regions far beyond what the soaring eagle has ever reached; while to the intrepid aeronaut himself, the scene of a world displayed beneath him is unquestionably the grandest, except that of the starry heavens, which mortal eye has ever compassed. To him even wide spread London, the queen of the cities of the earth, and a little world within itself, when viewed from a great elevation in the sky, appears but as a dusky patch upon a map, with the far-famed Thames winding there as a silvery line, and the magnificent temples and palaces scattered around appearing but as darker points rising out of the general mist of buildings, in which a million and a half of human beings reside. The first aeronautic expeditions astonished the world, and endless reveries passed through mens' minds of important uses to which the new discovery might be applied ; but more mature reflection, and now frequent trials have shown that the balloon, while furnishing philosophers with the opportunity of making some observations in elevated regions of the atmosphere, is still interesting chiefly as a philosophical toy. The French, under the Directory 202 PNEUMATICS. in 1796, attempted to use it as a military station, from which the position and motions of an enemy might be descried : but the plan was eventually abandoned. It has since been thought of as a means by which travellers might obtain information while penetrating into unknown countries, like the almost interlineable plain of Australasia. Although aeronauts, while aloft, have the power of making the balloon rise farther by*tb rowing out part of the sand-ballast which they carry with them, or of making it descend by opening a valve at the top, through which the hydrogen may escape, still they have no power of producing a lateral motion. The idea which yet strongly excites the minds of some projectors, that by wings or other means, a balloon may be directed in the sky nearly as a ship is directed on thesea, is not much more reasonable than to suppose that an insect, suspended to a huge block of wood, driven along at the rate of eight or ten miles an hour by river torrent, should have power to stop or sail against the stream. A man in a balloom would generally have to resist or change a motion exceed- ing fifty miles in an hour. A balloon which is only half full at the surface of the earth, becomes quite full when it has risen three miles and a half, because, at that altitude, air from below doubles its volume on account of the diminished pressure. A balloon, therefore, if quite distended on first rising, must let air escape as it ascends, or it will burst : this is true also of the drum of the human ear under the same circumstances, and in a contrary way under the opposite circumstances of descending in a diving-bell. The downy seeds of plants seen floating about upon the winds of autumn are not lighter than air, but have so much bulk and surface in proportion to their weight, that the friction upon them of the moving air, is greater than their weight, and carries them along. A sheet of paper made in some degree to resemble a balloon, by its having a little weight, representing the hanging car, attached by threads from its angles, is often seen rising at a street corner, to the delight of the boy who watches it. Its rise depends upon eddy winds or currents which the corner produces. The ascent ofjlame and smoke in the atmosphere, affords other examples of a lighter fluid rising in a heavier ; for both these are merely hotter air rising in the midst of colder. The phenomenon of flame is produced when a burning substance contains some ingredient capable, on being heated, of assuming the form of air or gas, which ingredient, or ascending, burns or combines with the oxygen of. the atmosphere, with intensity of action sufficient to produce a white heat. It is because charcoal and coke have nothing in them thus volatile, that they burn without flame, appearing like red-hot stones. The flame of a lamp or candle is merely the oil, wax, or tallow converted into gas, and allowed to burn as it is disengaged and rises. The same gas obtained by heating the oil, &c., in vessels which exclude the atmosphere, so as to prevent immediate combustion, and from which tubes lead to suitable receptacles, is the common oil-gas used for illumination. Smoke consists of all the dust and visible particles which are separated from the fuel without being burned, and are, moreover, light or minute enough to be carried aloft by the rising current of heated air ; but all that is visible of smoke is really heavier than air, and soon falls again as powdered chalk falls in water. In the receiver of an air-pump, where a candle has been extinguished by exhausting the air, the steam of smoke that continues FLOATING. FLAME AND SMOKE. 203 to pour from the wick after the exhaustion, is seen to fallen the pump-plate, because there is no air to support it. Chimneys quicken the ascent of hot air by keeping a long column of it together. A column of two feet high rises, or is pressed up with twice as much force as a column of one foot, and so in'proportion for all other lengths j just as two or more corks strung together and immersed in water, tend up- wards with proportionally more force than a single cork ; or as a long spear of light wood, allowed to ascend perpendicularly from a great depth in water, acquires a velocity which makes it dart above the surface, while a short piece under the same circumstances rises very slowly. In a chimney where one foot in height of the column of hot air is one ounce lighter than the same bulk of the external cold air, if the chimney be one hundred feet high, the air or smoke in it is propelled upwards with a force of one hundred ounces. In all cases, therefore, the draught, as it is called of a chimney, is pro- portioned to its length. The following facts are consequences of this truth. In. low cottages, and in the upper floors of houses, the annoyance of smoky rooms is much more frequent than were chimneys are longer. If there are two fires in the same room, or in any rooms open to each other, which have chimneys of different lengths, and of which the doors and windows are very close, so that the air to supply the draught cannot enter by them, the taller chimney will overpower the shorter, and cause it to smoke into the room ; just as the long leg of a syphon overcomes the short one, or as a long log of wood, held down in water by a cord passing from it round a pulley at the bottom to a shorter log also floating, will rise, and pull down the shorter log. | A long chimney, for the reasons above explained, causes a current of air to pass through the fire very rapidly, and it has the advantage also of acting more uniformly than any bellows or blowing machine. On these accounts, of fires of steam engines, and many others, it is the means of blowing generally preferred. The importance of length, in a chimney explains the remarkable appearance of some mining districts and modern English towns, where steam-engines abound. When we heap dying embers together, so that the hot air rising among them may become a mass or column of considerable altitude, this column has the effect of blowing them gently, and helps to light them up .again, A piece of burning paper thrown upon the top of a half-extinguished fire, often makes it blaze afresh, by causing a more rapid current of air to pass through it from below. The action or draught of a chimney, influenced as we have seen, by its length, depends also on the degree in which the air in it is heated, because this determines the dilitation, or comparative lightness, which makes the air ascend. In what are called open fire-places, such as those in the sitting-rooms of Britain, a large quantity of air directly from the apartment enters the chimney above the fire, and mixes with the hot air from the fire itself. This mixture ascends more slowly than if hot air alone entered, and in a proportion dependent on the degree of mixture. The effect of excluding a part of this colder air, is seen when a board or plate of metal is suspended across the opening of the chimney, so as to narrow the entrance : almost instantly a quicker action is produced, and the fire begins to roar as if blown by a bel- lows. This means is often used to blow the fire instead of bellows, or to cure a smoky chimney by increasing the draught. What is call a register 204 PNEUMATICS. stove is a kindred contrivance. It has a flap placed in the throat of the chim- ney, which serves to widen or contract the passage at pleasure. Because the flap is generally opened only enough to allow that air to pass which rises directly from the fire, the chimney receives only very hot air, and therefore acts well. The register stove often cures smoky chimneys : and by preven- ing the too ready escape of the moderately warmed air of the room, of which so much is wasted by a common fire-place, it also saves fuel. In what are called close fire-places, as those of steam-engines, or brewers' coppers, when the furnace door is shut, no air can enter the chimney but directly through the fire ; hence the action of such chimneys is very powerful. In a room with two fires, or in drawing rooms communicating with each other, although the chimneys be of equal length, that one over the best fire will act the most strongly ; and if the doors and windows of the apartment be so close as to prevent a sufficiency of air from entering by them to supply both fires, cold air will enter by that chimney which has the weakest fire, and the smoke from it will spread into the room. How often is an assembling dinner party annoyed by the smoke of a second drawing-room fire just lighted before their arrival, and which had therefore to contend with the. antagonist fire already in powerful action all the day. "While only one fire was lighted, the cold chimney was admitting the air to feed it, just as an open pane in the window would have done. A room may be so close that no air can find en- trance, and in such a case the smoke of its fire must all spread into the room. When all the windows and doors of a house fit so closely as not to admit air for the acting chimneys, the supply comes down the chimneys that are not in use. Inattention to this fact causes many a good chimney to incur the imputation of being smoky, because on the attempt being made to light a fire at it, the smoke at first is always thrown back. The truth is, that at the time when the servant begins to light the fire, there is a downward cur- rent in the chimney, repelling of course, any heated air and smoke that approaches it, and spreading them over the whole house; but were the room door to be shut for a few minutes, so as to cutoff communication with the other drawing chimneys in the house, while at the same time the windows were opened, the chimney would act at once ; and when sufficiently heated, would continue to act in spite of the others, as well as they. There are some cases of smoky rooms not to be so easily corrected as what we have now mentioned. When a low house adjoins a lofty house, the wind blowing towards the latter, is obstructed and becomes a gathering or conden- sation of air against the wall ; and if the top of a low chimney be there, the compressed air enters it and pours downwards. The same happens occasionally from the proximity of trees or rocks. In such cases, to avoid the influence, the chimneys of the low houses are often made very lofty. Again, whenever, from the nature of buildings, eddies of wind occur, or unequal pressures, as at street corners, &c., the chimneys around do not act regularly. It is pro- verbial, that corner houses, or those at the end of a row, are smoky houses ; and we see the uniformity of architecture in a street often destroyed by the necessity of lengthening the chimneys of the houses at the extremities. When smoke is found descending into a room where there is no fire, the empty chimney is serving as an inlet for air to the house, while the smoke of a neighboring chimney is passing closely over the top of ijb. In summer, when fires are not in use, there is often a strong smell of soot perceived in the apartments during the whole of the day, but which ceases at night. The reason is, that during the day the chimney is colder than the external air, and by condensing the air which enters it, causes a downward FLOATING. FLAME AND SMOKE. 205 current through the soot. During*he night, again, when the external air becomes colder, owing to the absence of the sun, the chimney, by retaining the heat absorbed during the day, is hot enough to warm the air in it, and to cause an upward current. These currents, in chimneys left open during the days and nights of summer, are almost as regular as the land and sea breezes of tr6pical countries. All these remarks prove how important it is to be able to conceive clearly of the motions going on, according to the simple laws of matter, in the invisible air around us. Were such subjects better and more generally understood, many prevalent errors in the arts of life, influencing much the comforts and health of the community, would soon be corrected. If we are filled with admiration on discovering how perfectly the simple law of a lighter fluid rising in a heavier, provides a constantly renewed sup- ply of fresh air to our fires, which supply we should else have to furnish by the unremitted action of some expensive blowing apparatus, still more must we admire that the operation of this law should effect the more important purpose of furnishing the ever renewed supply of the same vital fluid to breathing creatures. The air which a man has once respired becomes poison to him ; but because the temperature of his body is generally higher than that of the atmosphere around him, as soon as he has discharged any air from the lungs, it ascends completely away from him into the great purify- ing laboratory of the atmosphere, and new air takes its place. No art or labor of his, as by the use of fans or punkas, could have done half so well what this simple law unceasingly and invisibly accomplishes, and accom- plishes without effort or even attention on his part, and in his sleeping as in his waking hours. Truly in this, may he be said to be watched over by a kind Providence. The warming and ventilating of houses, is an important art, founded chiefly on the foregoing considerations, and at present too little understood, not only by the public at large, but even by medical practitioners, whose management of disease, though judicious in other respects, is often rendered vain by error or omission in this. Excellent fuel is so cheap in Britain, owing to the profusion which beds of rich coal are scattered in it, that a careless domestic expenditure has arisen ; which, however, instead of securing the comfort and health that might be expected, has led to plans of warming which often prove destruc- tive to both. The mischief lies chiefly in the unsteadiness or fluctuations of our domestic temperature ; for in still colder countries, and where fuel is more expensive, as in the north of continental Europe, the necessity for economy has led to contrivances which give steady temperature and impunity. In cold countries, to retain and preserve the heat once obtained, the houses are made with thick walls, double windows, and nice fittings ; and, more- over, with close stoves or fire-places, which draw their supply of air, not from the apartments where they are placed, wasting the temperate air of these, but directly from without. Thus fuel is saved to a great extent, and a uniformity of temperature is produced, both as regards the different parts of the room, so that the occupiers may sit with comfort where they please, and as regards the different times of the day, for the stove being once heated in the morning, often suffices to maintain a steady warmth until night. The temperature can be carried to any required degree, 'and sufficient ventilation is easily effected. In England, again, the apartments, with their open chimneys, may be 206 PNEUMATICS. compared to great air funnels, constancy pouring out their warm contents through a large opening, and constantly requiring to be replenished. They thus waste fuel exceedingly, because the chimney being large enough to allow a whole room-full of air to pass away in two or three minutes, the air of the room has to be warmed, not once in the course of the day, but very many times. The temperature in them is made to fluctuate by the slightest causes, as the opening a door, the omitting to stir the fire, &c. The heat is very unequal in different parts of the room, rendering it necessary in general for the company to sit near the fire ; where they must often submit to be almost scorched on one side, while they are chilled on the other. There is generally a warm stratum of air above the level of the chimney-piece, sur- rounding, therefore, the upper part of the bodies of persons in the room, while a cold stratum below envelopes the sensitive feet and legs. As a very rapid current is constantly ascending in the chimney, a corresponding supply must be entering somewhere ; and it can only enter by the crevices and defects in the doors, windows, floors, &c. : now there is nothing more dangerous to health than to sit near such inlets, as is proved by the rheumatisms, stiff necks and catarrhs, not to mention more serious diseases, which so frequently follow the exposure. There is an old Spanish proverb, thus translated, " If cold wind reach you through a hole, Go make your will and mind your soul," which is scarcely an exaggeration. Consumption is the disease which carries off a fifth or more of the persons born in Britain; owing in part, no doubt, to the changeableness of the exter- nal climate, but much more to the faulty modes of warming and ventilating the houses. To judge of the influence of temperature in producing this disease we may consider, that miners who live under ground, and are always, therefore, in the same temperature, are strangers to it, while their brothers, and relatives, exposed to the vicissitudes above, fall victims, that butchers and others, who live almost constantly in the open air, so as to be hardened by the exposure, enjoy nearly equal immunity, that consumption is scarcely known in Russia, \ihere close stoves and houses preserve a uniform tempera- ture within doors, while fit clothing gives safety on going out, and that in all countries and situations, whether tropical, temperate or polar, the fre- quency of the disease bears relation to the degree and manner of change. We may here remark, also, that it is not consumption alone which springs from changes of temperature, but a great proportion of acute diseases, and particularly of the common winter diseases of England. There are a few cases of these in which the invalid has not to remark, that if he had avoided cold or wet on some certain occasion, he might yet have been well. Wnile temperature is thus so frequently an original cause of disease, it is also a circumstance of the very highest importance in the treatment, as is proved by every fact bearing upon the question. We may, therefore, at first wonder that it should be so negligently and unskilfully controlled as we often see it 'j disease and death being thence allowed to lurk, as it were, undis- turbed in the sanctuaries of our homes : but when we reflect on the subtile and invisible nature of air and heat, and that the science which detects their agencies has been hitherto so little an object of general study, and is, indeed, of modern discovery, the fact is accounted for. In England', the open fire-place is so generally in use for common dwell- ings, and the cheerful 'blaze is accounted so essential to the comforts of the winter days and long evenings, that it would be difficult to persuade persons FLOATING. WARMING AND VENTILATING. 207 to abandon it : let us hope, then, that when the subject which we are now discussing comes to be better and more generally understood, the open fire, with close flooring, better for double windows, doors that fit well, register stoves, and good general management, may be rendered almost as efficient for warming, and as safe to health, as any other contrivance. The following considerations present themselves in this place: Small rooms in winter are more dangerous to health than large ones, because the cold air, entering towards the fire by the doors and windows, reaches the per- sons in the room before it can be tempered by mixing with the warmer air already around them. Stoves in halls and stair-cases are useful, because they warm the air before it enters the rooms ; and they prevent the hurtful chills often felt on passing through a cold stair-case from one warm room to another. It is important to admit no more cold air into the house than is just required for the fires and for ventilation ; hence there .is a great error in the common practice of leaving all the chimneys that are not in use quite open, each admitting air as much as a hole in the wall, or an open pane in the window would do. Perhaps the best mode of admitting air to feed the fires is through tubes, leading directly from the outer air to the fire-place, and provided with what are called throttle-valves, for the regulation of the quan- tity ; the fresh air admitted by them being made to spread in the room either at once, or after having been warmed during its passage inwards, by coming near the fire. In a very close apartment, ventilation must be ex- pressly provided for by an opening near the ceiling, through which the impure air, rising from the respiration of the company, may pass away. With an open fire the purpose is effected, although less perfectly, by the frequent change of the whole air of the room which that construction occasions. With a view to have, in rooms intended for invalids, the most perfect security against cold blasts and fluctuations of temperature, and still to retain the so much valued appearance of the open fire, a glazed frame or window may be placed at the entrance to the chimney or stove, so as completely to prevent the passage of air from the room to the fire. The room will then be warmed by the fire through the glass, nearly as a green-house is warmed by the rays of the sun. It is true that the heat of combustion does'not pass through glass so readily as the heat of the sun ; but the difference for the case supposed is not important. The glass of such a window must, of course, be divided into small panes, and supported by a metallic frame-work to resist the heat ' } and there must be a flap or door in the frame- work, for the purpose of admitting the fuel and stirring the fire. Air must be supplied to the fire, as described above, by a tube leading directly from the external atmosphere to the ash-pit. The ventilation of the room may be effected by an opening into the chimney near the ceiling; and the temperature may be regulated with great precision. by a valve placed in this opening, and made to obey the dilatation and contraction of a piece of wire affixed to it, the length of which will always depend on the temperature of the room. The author contrived the arrangements here described, for the winter residence of a person threatened with consumption, and the happy issue of that particu- lar case, and of others treated on similar principles, has led him to doubt whether many of the patients with incipient consumption who are usually sent to warmer climates, and who die there after suffering hardships on the journey, and distress from the banishment sufficient to shake even strong health, might not be saved by judicious treatment in properly warmed and ventilated apartments, under their own roofs, and in the midst of affectionate kindred. And if a boy be almost certainly secured from consumption by 208 PNEUMATICS. being made a miner or a butcher, may we not hope that, when all the influ- encing circumstances come to be better understood, something of the same immunity may be obtained for persons in all the professions- and conditions of civilized society ? It must not be supposed that the remarks made in this section exhaust even nearly the very important subject of temperature as affecting health. The questions of clothing, of hot and cold bathing, of exercise, and others, equally belong to it, but the consideration of them falls under other depart- ments of study. Winds or currents in the atmosphere are also phenomena, in a great measure dependent on the law, that lighter fluids rise in heavier. As oil let loose under water is pressed up to the surface and swims, so air near the surface of the earth, when heated by the sun, rises to the top of the atmosphere, and spreads there, forced up by the heavier air around; this heavier air rushing inwards, constitutes the wind felt at the surface of the earth. The cross currents in the atmosphere arising as now described, are often rendered evident by the motion of clouds or balloons. If our globe were at rest, and the sun were always beaming over the same part, the earth and air directly under the sun would become exceedingly heated, and the air there would be constantly rising like oil in water, or like the smoke from a great fire ; while currents or winds below would be pour- ing towards the central spot, from all directions. But the earth is constantly turning round under the sun, so that the whole middle region or equatorial belt may be called the sun's place : and therefore, according to the principle just laid down, there should be over it a constant rising of air, and constant currents from the two sides of it, or the north and south, to supply the ascent. Now this phenomenon is really going on, and has been going on ever since Jthe beginning of the world, producing the steady winds of the northern and southern hemispheres, called trade winds, on which in most places within thirty degrees of the equator, mariners reckon almost as con- fidently as on the rising and setting of the sun himself. The trade winds, however, although thus moving from the poles to the equator, do not appear on the earth to be directly north and south, for the eastward whirling, or diurnal rotation of the earth, causes a wind from the north to appear as if coming from the north-east, and a wind from the south as if coming from the south-east. This fact is illustrated by the case of a man on a galloping horse, to whom a calm appears to be a strong wind in his face ; and if he be riding eastward, while the wind is directly north or south, such wind will appear to him to come from the north-east, or south-east : or again, is illustrated by the case of a small globe made to turn upon a per- pendicular axis, while a ball or some water is allowed to run from the top of it downwards; the ball or water will not immediately acquire the whirling motion of the globe, but will fall almost directly downwards, in a track which, if marked upon the globe, will appear not as a direct line from the axis to the equator, that is, from north to south, but as a line falling obliquely. Thus, then, the whirling of the earth is the cause of the oblique and west- ward direction of the trade winds ; and not, as has often been said, the sun drawing them after him. The reason why the trade winds at their external confines, which are about 30 degrees from the sun's place, appear almost directly east } and become FLOATING. WINDS. 209 more nearly north and south as they approach the central line, is, that at the confine they are like 'fluid coming from the axis of a turning wheel, and which has approached the circumference, but has not yet acquired the velocity of the circumference ; while, nearer the line, they are like the fluid after it has for a considerable time been turning on the circumference, and has acquired the rotary motion there, consequently appearing at rest as regards that motion, but still leaving sensible any motion in a cross direction. While, in the lower regions of the atmosphere, air is thus constantly flowing towards the equator and forming the steady trade winds between the tropics in the upper regions, there must, of course, be a counter-current distributing the heated air again over the globe : accordingly, since reasoning led men to expect this, many striking proofs have been detected. At the summit of the Peak of Teneriffe, observations now show that there is always a strong wind blowing in a direction contrary to that of the trade wind on the face of the ocean below. Again, the trade winds among the West India Islands are constant, yet volcanic dust thrown aloft from the Island of St. Vincent, in the year 1812, was found, to the astonishment of the inhabitants of Barbadoes, hovering over them in thick clouds, and falling, after corning more than 100 miles directly against the strong trade wind, which ships must take a circuitous course to avoid. Persons sailing from the Cape of Grood Hope to St. Helena, have often to remark that the sun is hidden for days together, by a stratum of dense clouds passing southward high in the atmosphere } which clouds consist of the moisture raised near the equator with the heated air, and becoming condensed again as it approaches the colder regions of the south. Beyond the tropics, where the heating influence of the sun is less, the winds occasionally obey other causes than those we have now been con- sidering, which causes have not yet been fully investigated. The winds of temperate climates are in consequence much less regular, and* are called variable ; but still, as a general rule, whenever air is moving towards the equator, from the north or south poles where it was at rest, it must have the appearance of an east wind, or a wind moving in the contrary direction of the earth itself, until it has gradually acquired the whirling motion of that part of the surface of the earth on which it is found; and again, when air is moving from the equator, where it had at last acquired nearly the same motion as that part of the earth, on reaching parts nearer the poles, and which have less eastward motion, it continues to run faster than they, and becomes a westerly wind. In many situations beyond the tropics, the westerly winds, which are merely the upper equatorial currents of air falling down, are almost as regular as the easterly winds within the tropics, and might also be called trade winds : witness the usual shortness of the voyages from New York to Liverpool, and the length of those made in the contrary direction. North of the equator, then, on earth, true north winds appear to be north-east, and true south winds appear to be south-west : which are the two winds that blow in England for three hundred days of every year. In southern climates the converse is true. While the sun is beaming directly over a tropical island, he warms very much the surface of the soil, and, therefore, also, the air over it j but the rays which fall upon the ocean around penetrate deep into the mass, and produce little increase of superficial temperature. As a consequence of this, there is a rapid ascent of hot air over the island during the day, and a cooler wind blowing towards its centre from all directions. This wind. constitutes the refreshing sea-breeze of tropical islands and coasts. A person must have been among these, to conceive the delight which the sea-breeze brings after 14 210 PNEUMATICS. the sultry stagnation which precedes it. The welcome ripple shorewards is first perceived on the surface of the lately smooth or glassy sea ; and soon the whole face of the sea is white with little curling waves, among which the graceful canoe, lately asleep on the water, now shoots swiftly along. During the night a phenomenon of opposite nature takes place. The surface of the earth then no longer receiving the sun's rays, is soon cooled by radiation, while the sea, which absorbed heat during the day, not on the surface only, but through its mass, continues to give out heat all night. The consequence is, that the air over the earth becoming colder than that over the sea, sinks down, and spreads out on all sides, producing the land- freeze of tropical climates. This wind is often charged with unhealthy exhalations from the marshes and forests, while the sea-breeze is all purity and freshness. Many islands and coasts would be absolutely uninhabitable but for the sea-breeze. The peculiar distribution of land in the Asiatic part of the globe, produces the curious effect there of a sea-breeze of six months, and a land-breeze of six months. The great continent of Asia lies chiefly north of the line, and during its summer, the air over it is so much heated, that there is a constant steady influx from the south appearing south-west, for the reason given in a preceding page; and during its winter months, while the sun is over the southern ocean, there is a constant land breeze from the' north appearing, for a like reason, north-east. These winds are called monsoons ; and if their utility to commerce were to be a reason for a name, they also deserve the name of trade winds. In early periods of navigation, they served to the mariner the purpose of compass, as well as of moving power ; and one voyage outward, and another homeward with the changing monsoons, filled up his year. On the western shores of Africa and America, also, the trade winds are interfered with by the heating of the land; but much less so than in Asia, and always in accordance with the laws now explained. The frightful tornadoes, or whirlwinds, which occasionally devastate certain tropical regions, making victims of every ship or bark caught on the waters, and the shore gusts or squalls met with every where, are owing to some sudden chemical changes in the atmosphere, not yet fully understood. The Pneumatic Trough and Gasometer of the chemist are contrivances constantly displaying the truth now under consideration, " that a lighter fluid is pushed up and floats on a heavier." They are important parts of the apparatus for operating on substances while in the form of air. The trough a may be made of metallic plate, or of wood lined with metal, and of any convenient size. It is nearly filled Fig. 106. with water, and has at one end about an inch under the surface of the water, a shelf on which jars or vessels, as b and c, may rest. Any particular air or gas is preserved separate from the atmosphere, by being placed in one of these jars with the mouth downwards. The gas is passed into the jar by the operator first immers- ing the jar in the trough, so as to fill it with water and to expel the common air from it; and then holding its mouth over the gas while rising under the water from another vessel or pipe : FLOATING. GAS APPARATUS. 211 Fig. 107. CL -s a ci d represents a long-necked vessel, used to contain the ingredients for the pro- duction of gases by chemical action. The gas of course rises to the top of the jar b, and gradually'displaces the water. During the operation of filling, the jar may be supported by the hand or by resting on the shelf; in the latter case the gas is allowed to rise into it through a hole in the shelf, pro- vided with a small funnel gaping downwards to catch the air more readily. The shelf may have room on it for many jars, and it may have more holes than one ; and if the gas under operation be such that water absorbs or changes it, some other liquid, as mercury, may be used instead of water. A gasometer or gas-holder, is merely a larger jar or vessel as or, dipping into water, with its mouth downwards, in a trough of its own shape, 6 c, and so sup- . ported or counterpoised by a weight at d, over pullies, that very little force suffices to move it up or down. Air forced into it through a pipe /opening under it, causes it to rise or float higher in proportion to the quantity. The air is made to pass from it again when wanted, either through the same tube or through another as e. The huge gasometers, exceeding in size an ordinary house, and containing the supply of gas for the lamps of a town, are vessels suspended as above represented, in great pits or troughs, filled with water. The gas issues with force proportioned to the downward pressure of the containing vessel, which may be nicely regulated in a variety of ways, and is generally made to equal the action of a column of water of two inches in height; that is to say, such, that a pipe issuing from the gas holder, and dipping into water at its other end, shall allow gas to escape, if immersed less than two inches perpendicularly. It would be encroaching on the province of the chemist to treat here par- ticularly of the substances which most generally exist in the aeriform state ; but to give an increased interest to the description of the gas apparatus, a few leading facts may be mentioned. Of about fifty distinct substances known as the materials of our globe, five, when uncombined, and under common circumstances of heat and pressure, exist as air or gases The water used to fill the apparatus above described is a compound of two of the substances, viz., oxygen and hydrogen. By directing an electrical current through water, it is gradually decomposed, and from one side, a stream of aeriform oxygen may be received, and from the other a stream of hydrogen The two gases may be again united to form water, by mixing them in a proper vessel, and passing an electric spark through them. They combine with explosion. This oxygen, so called from its relation to acids, (the name consisting of two Greek words, signifying acid and to form,) has been accounted, for many reasons, the most important substance in nature. It forms eight- ninths, by weight of the ocean ; one-fourth of the atmosphere ; and perhaps one-fourth of the solid matter of the globe : possibly, therefore, although most persons think of it only as an air or gas, there is not a millionth part of the quantity of oxygen in the world existing as air. It unites readily with most other substances, and generally with such intense action as to 212 PNEUMATICS. produce the phenomena of fire or combustion;, the word combustible chiefly apply to substances that quickly combine with oxygen. Oxygen assumes a singular variety of character in its different combina- tions. Thus with hydrogen, it forms water; with lead, it forms the sub- stance called red-lead ; with nitrogen, in one proportion, it forms atmospheric air, in another proportion, the nitrous oxide, or what is called the laughing gas, in a third, the acid called aqua fortis ; with sulphur it forms the sulphuric acid or oil of vitriol; with iron, and all metals it forms their ores called oxides : and so forth. But the most important character in which we know it, is as that ingredient of our atmosphere, without which animals and vegetables cannot live, and fire cannot burn. Oxygen, from this part of its history, was long named vital or pure air. Pure oxygen, in the state of air is a little heavier than common air; but, when holding a quantity of charcoal in solution, it forms aeriform carbonic acid, which is nearly twice as heavy as common air, and may be poured out of one vessel into another like water. Carbonic acid is what issues from soda-water, brisk ale, champagne, &c., while they sparkle. If drawn into the lungs in breathing, it is fatal to life. A charcoal fire left in a close room with sleeping persons, has often been fatal to them, because carbonic acid gas is the product of the combustion. So likewise, houseless wretches in winter lying down in a bricktnaker's field to leeward of a burning-heap of bricks, often fall asleep for ever. The famous Grotto del Cane, in Italy, is a cavern always full of carbonic acid, which springs into it from below, as water springs into a well, and runs over like water from a well : it received its name from the circumstance of dogs dying instantly when thrown into it. Carbonic acid rising in fermentation has often proved fatal to persons leaning over the edge of fermenting vats. It is common to see a rat die instantly, in the attempt to run a plank laid across the mouth of a fermenting tub. Hydrogen, the other ingredient of water, so called from its relation to water (the name consists of the Greek words for water and to form,) when in the state of air, is sixteen times as light as oxygen. With it balloons are filled. When it holds in solution a certain quantity of carbon or charcoal it becomes the common gas used for illumination, and is the fire-damp of mines, of which the burning and explosion are so terrible. It forms one- ninth of the ocean, and much of the animal and vegetable bodies. Nitrogen, so called from its relation to nitric acid, is the third and last substance which we shall mention. It is what remains of the atmosphere when the oxygen is removed. It forms about four-fifths of the atmosphere, one-fourth of the animal flesh, and is found in small quantities in the other combinations. It will not support life by itself, and therefore formerly was called azote : with a larger portion of oxygen, it forms nitric acid or the aquafortis of old. The last few paragraphs may serve to show how many of the manipula- tions of chemistry are directed by the principles of physics or mechanical philosophy; and therefore, how essential to the chemist the preliminary study of physics becomes, DISCHARGE FROM APERTURES. 213 PART III. OR THE PHENOMENA OF FLUIDS. ( CONTINUED. ) SECTION III HYDRAULICS PHENOMENA OF FLUIDS IN MOTION. ANALYSIS OF THE SECTION. Whether the particles of matter exist -in the form of solid or fluid, the cir- cumstance does not affect their properties of INERTIA and GRAVITY. Hence liquids and airs, in proportion to their quantity, resist, receive, and impart motion, and have weight and friction, as is true of solids. This is seen in the phenomena of 1. Fluids issuing from vessels, or moving in pipes and channels. 2. Waves. 8. Fluids resisting the motion of bodies immersed in them; or themselves moving against other bodies. 4. Fluids lifted, or moved in opposition to gravity. "Fluids issuing from vessels, or moving in channels. 1 ' WATER admitted to a tube ascending from near the bottom of a reservoir will rise in it, as already explained, to the level of the liquid-surface in the reservoir. If such a tube be afterwards cut off, except a small part at the bottom, then prepared as a jet-pipe, the water will spout from this still to the same height, with a certain deduction for the resistance of the air and friction. Now as a body shot upwards to any height has that velocity in departing, which it again acquires by falling back to the same place or level, (with a certain deduction for the resistance of the air,) as explained at page 60, it follows that fluid issues from any orifice in a reservoir with velocity equal to what a body acquires in falling as far as from the level of the fluid surface in the reservoir to the orifice. By referring then to the law of fall- ing bodies, as explained at page 50, we may learn the velocity of the issue of water in any case, and therefore t the quantity delivered by an opening of a given magnitude. 214 HYDRAULICS. Thus, a body by gravity falls sixteen feet in the first second, with speed gradually increasing, and at the end of the second has a velocity of thirty-two feet per second; therefore a reservoir with an. opening of an inch square at sixteen feet below the water's surface, will deliver, in one second of time, with a certain deduction for resistance of air, friction, &c., thirty-two feet of a jet of water of an inch square ; and according to the same rule, an opening at four times the depth should deliver a double quantity ; at nine times the depth, a triple quantity ; and so on, as really happens. An inquirer is at first surprised that the quantity should not be quadruple, where the height of column or pressure forcing it out is quadruple, ninefold when the pressure is ninefold, &c., but on reflection, he may perceive that the real effects, as stated above, are still exactly proportioned to the causes ; for when only twice as much water is forced out in the same time, there is still an effect, four times as powerful, because each particle of the double quantity issues with twice the force or velocity, and increase of velocity costs just as much force as increase of quantity. Similar reasoning holds with respect to the triple or other quantities. Because a body shot upward with a double velo- city gains a quadruple height, ( see page 60, ) the jet issuing with only double velocity from four times the depth, still reaches the level of the surface of the reservoir. The knowledge of this rule for discharging orifices is of the greatest importance in the construction of water-works, because when joined with other rules assigning the effects of friction, bending, unequal width, &c., in pipes, it ascertains the quantity of water which a conduit of any magnitude, length and slope, will deliver. It is a curious fact, that more water issues from a vessel through a short pipe, than through a simple aperture of the same diameter as the pipe; and still more if the pipe be funnel-shaped, or wider towards its inner extremity. The explanation is, that the issuing particles .coming from all sides to escape, cross and impede each other in rushing through a simple opening, as is proved by the narrow neck which the jet exhibits a little beyond the opening ; but in a tube, this narrowing of the jet cannot happen without leaving a vacuum around the part, and the pressure of the atmosphere, re- sisting the vacuum, causes a quicker flow. The funnel-shape again leads the water by a more gradual inclination to the point of exit, and thus con- siderably prevents the crossing among the particles ; besides that, because its mouth surrounds the narrow neck of the jet, it allows that part to be deemed the commencement of the jet. Another remarkable effect of atmospheric pressure on running liquids is, that in a tube of considerable length, descending from the reservoir, it much quickens the discharge. Water naturally falls like any other body with accelerating velocity, but if it so fall in a tube which it fills like a piston, either portions of it below must outstrip portions above, leaving vacuous spaces between, or water from above must be pressed into the tube by some other force than its weight. Now the atmospheric pressure becomes this force, and it prevents a vacuum, partly by impelling water more rapidly into the top of the tube, and partly by resisting the discharge from below. The forcing in of the water at the top of the tube causes that depression of the water surface in the reservoir over it, which becomes more conspicuous as the depth in the reservoir diminishes, and at last is a deep hole in the water extending far into the tube, and sometimes even as in a common funnel extending quite through. The friction or resistance which fluids suffer in passing along pipes is DISCHARGE FROM APERTURES. 215 i much higher than might be expected. It depends on the cohesion of the particles to the surface of the pipe and among one another, and on the par- ticles near the outside being constantly driven from their straight course by the irregularities in the surface of the pipe. An inch tube of two hundred feet in length, placed horizontally, is found to discharge only a fourth part of the water which escapes by a a simple aperture of the same diameter. All passing along tubes is still more retarded. A person who erected a great bellows at a water-fall, to blow a furnace two miles off, found that his apparatus was totally useless. When gas lights were first proposed, some engineers feared that the resistance by friction to the passing air would be fatal to the enterprise. Higher temperature in a liquid increases remarkably the quantity dis- charged by an orfice or pipe, apparently by diminishing that cohesion of the particles which exists in certain degrees in all liquids and affects so much their internal movement. The additition of 100 degrees of heat will, in certain cases, nearly double the discharge. The flux of water through orifices under uniform circumstances is so steady, that before the invention of clocks and watches, it was employed as a means of measuring time. The vessels were called clepsydrae,. That of Ctesibius is famous, in which the issuing water took the form of tears from the eyes of a figure, deploring the rapid passing of precious time ; and these tears being received into a fit vessel, gradually filled it up and raised another floating figure, who pointed to the hours marked on an upright scale. This vessel was daily emptied by a syphon, when charged to a certain height, and its discharge worked machinery which told the month and the day. The common hour-glass of running sand is another modifica- tion of the same principle, with this remarkable difference, however, that depth of the sand does not quicken the flux. The progress of water in an open conduit, such as the channel of a river or acqueduct, is influenced by friction, &c., in the same manner as in close pipes. But for this, a river like the Rhone, drawing its waters from the elevation of 1,000 feet above the level of its mouth, would pour them out, with the velocity of water issuing from the bottom of a reservoir, 1,000 feet deep; that is to say, at the rate of about 170 miles per hour. The ordinary flow of rivers is about three miles per hour, and their channels slope three or four inches per mile. The velocity of a water current is easily ascertained by immersing in it an upright tube, of which the bottom bent at right angles becomes an open mouth turned towards the stream. The water in the tube will stand above the surface of the stream, as much as would Fig. 108. be necessary in a reservoir, according to the explanation j ( given above, to cause a velocity of jet equal to the velocity ct of the stream. A modification of this contrivance may be made to measure the velocity of the wind. A common mode of telling the velocity of an open stream, is to observe with a stop-watch the progress of a body floating in some part of it from which its medium speed maybe known; and know- ing that speed and the depth and width of the channel the quantity delivered in a given time becomes a matter of sim- pie calculation. The speed of the wind may be ascertained by observing how long the shadow of a cloud takes to pass across a field of known dimensions. The friction of water moving in water is such, that a small stream directed 216 HYDRAULICS. through a pool, with speed enough to rise' over the opposite bank, will soon empty the pool. Extensive fens have been drained on this principle. The friction between air and water is also singularly strong, and is proved on a great scale by the magnitude of the ocean-waves, which is a consequence of it ; and on a small scale, by the amusing experiment of making a light round body dance or play upon the summit of a water-jet a chief cause of its remaining there being, that the current of air which rises around the jet by reason of the friction, presses it inward again, whenever it inclines to fall over. Oil thrown upon the surface of water, soon spreads as a film over it. and defends it from farther contact and friction of the air. If oil be thus spread at the windward side of a pond where the waves begin, the whole surface of a pond becomes as smooth as glass ; and even out at sea, where the commencement of the waves cannot be reached, oil thrown upon them smooths their surface to leeward of the place, and prevents their curling over or breaking. It is said that boats having to reach the shore through a raging surf, have been preserved by the crews first spilling a cask of oil in the offing. The most magnificent examples that ever existed, or probably ever will ' exist of artificial water-courses, were the acqueducts of ancient Borne, about twenty in number. Several of them exceeded forty miles in length, passing Ihrough hills in their way, and resting on tiers of splendid arches across the valleys. They were constructed of such durable materials, and so skilfully, that the principal of them remain perfect to this day. Considered as one object, they rank, in point of magnitude, with any other work of human labour, not excepting the pyramids of Egypt. While the acqueducts are cited as specimens of grandeur, we may mention the fountains in the gardens of France and Italy as specimens of beauty. Those at Versailles are well known. In them the most magical effects are produced by varying the ways in which water is made to spout from orifices. In one place it is seen darting into the air as a single upright pillar : in others many such pillars rise together, like giant stalks of corn ; sometimes an inclination given to the jets makes them bend so as to form beautiful arches, of which a portion appear as the roofs of apartments built of water while others mingle together with endless variety : here and there water-throwing wheels throw out spiral streams, and hollow spheres with a thousand openings are the centres of immense bushes or trees of silvery boughs. Such effects amidst cascades, smooth lakes, and scenes of lovely landscapes, constitute a whole as enchanting, perhaps, as art by moulding nature has ever produced. " Waves." The form, magnitude and a velocity of waves, are subjects admitting of deep mathematical research ; and are rendered the more interesting, because certain phenomena of sound and light are of kindred nature. Here, how- ever, they must be treated with great brevity. A stone thrown into a smooth pond, causes a succession of circular waves to spread from the spot where it falls as a common centre. They become of less elevation as they expand, and each new one is less raised than the pre- ceding, until gradually the liquid mirror becomes again perfect as before. Several stones falling at the same time in different places, cause crossing circles which, however, do not disturb the progress of one another a phe- nomenon seen in beautiful miniature at each leap of the little insects which cover the surface of our pools in the calm hours of summer. The rationale WAVES. 217 of the formation of waves in such cases is as follows : When the stone falls into the water, because the liquid is incompressible, a part of it is displaced laterally, and becomes an elevation or circular wave around the stone. This wave then spreads outward in obedience to the laws of fluidity, already explained, and the circle is seen to widen. In the meantime, where the stone descended, a hollow is left for a moment in the water, but owing to the surrounding pressure, is soon filled up, chiefly by a sudden rush from below. The rising water does not stop, however, at the exact level of that around, but like a pendulum sweeping past the centre of its arc, it rises almost as far above the level as the depression was deep. The central eleva- tion now acts as the stone did originally, and causes a second wave, which pursues the first ; and when the centre subsides, like the pendulum still, it sinks again almost as much below the level as it had mounted above : hence it has to rise again, again to fall, and so on for many times, sending forth a new wave at each alternation. Owing to the friction among the particles of the water, each new wave is less raised thten the preceding, and at last the appearance dies away. A wave passing through any gap or opening, spreads from it as a new centre ; and a wave coming against a perpendicular surface of wall or rock, is completely reflected from this, and acquires the appearance of coming from a point as far beyond the reflecting surface, as its real origin or centre is distant on the side where it is moving. So absolutely level is a liquid surface, and so sensitive or mobile, that the effect of any disturbing cause is perceived at great distances. A boat rowed across a still lake, ruffles its surface to a great extent ; and although the widening waves become at last such gentle risings as not to*be perceptible to the eye, they still produce a rippling noise where they fall among the pebbles on shore. In seas liable to sudden but partial hurricanes, the roar of breakers on distant coasts often tells of the storm which does not other- wise reach them. The author once, in the eastern ocean, had an opportunity of contemplating waves of extraordinary magnitude rolling along during a gloomy calm, and therefore with unbroken surface, appearing like billows of molten lead. At that very time, about a hundred and fifty miles to the north-east, four of the finest ships of the India Company were perishing in a storm. In the polar seas which are comparatively tranquil, because partially defended from the wind by the floating islands of ice, a few sudden waves are occasionally observed, and quickly all is calm again. Such a phenomenon announces, that the occurrence described at page 153 has happened some- where, of an island of ice turning over, when the place of its centre of gravity is changed by partial melting. The common cause of waves is the friction of the wind upon the'surface of the water. Little ridges or elevations first appear, which, by continuance of the force, gradually become loftier and broader, until they are the rolling mountains seen where the winds sweep over a great extent of water. The heaving of the Bay of Biscay, or still more remarkably, of the open ocean beyond the southern capes of America and Africa, exhibits one extreme, and the stillness of the tropical seas, which are sheltered by near encircling lands exhibits the other. In the vast archipelago of the east, where Borneo and Java and Sumatra lie, and the Molucca Islands and the Philippines, the sea is often fanned only by the land and sea breezes, and is like a smooth bed in which these islands seem to repose in bliss islands in which the spice and pefume gardens of the world are embowered, and where the bird of paradise has its home, and the golden pheasant, and a hundred other birds of brilliant 218 HYDRAULICS. plumage, among thickets so luxuriant, and scenery so picturesque, that European strangers find there the fairy land of their youthful dreams. One who has visited these islands in his early days, may perhaps be pardoned for thus adverting to their beauties. In rounding the Cape of Good Hope, waves are met with, or rather a swell, so vast, that a few ridges and a few depressions occupy the extent of a mile. But these are not so dangerous to ships, as what is termed a shorter sea, with more perpendicular waves. The slope in the former is compara- tively gentle, and the rising and falling are much less felt ; while among the latter, the sudden tossing of the vessel is often destructive. When a ship is sailing directly before the wind, over the long swell now described, she advances as if by leaps ; for as each wave passes, she is first descending head- long on its front, acquiring a velocity so wild that she can scarcely be steered ; and soon after, when it has glided under her, she appears climbing on its back, and her motion is slackened almost to rest, before the following wave arrives. To a passenger perched at such a time on the extremity of the bowsprit, and looking back on the enormous body of the ship, with perhaps its thousands of a crew, a hundred feet behind him, heaved by those billows as a cork is on a ruffled lake, the scene is truly sublime. When a coming wave lifts the stern and in the same decree depresses the bow, he is deep in the hollow or valley between the waves, and sees only the ship rushing head- long down towards him as if to be engulphed - r but soon after, when the stern is down, and the bow is raised, he looks from his station in the sky upon an awful scene beneath him and around. The velocity of waves has relation to their magnitude. The large waves just spoken of, proceed at the rate of from thirty to forty miles an hour. It is a vulgar belief that the water itself advances with the speed of the wave, but in fact the form only advances, while the substance, except a little spray above, remains rising and falling in the same place, with the regularity of a pendulum. A wave of water, in this respect, is exactly imitated by the wave running along a stretched rope when one end is shaken ; or by the mimic waves of our theatres, which are generally undulations of long pieces of car- pet moved by attendants. But when a wave reaches a shallow bank or beach, the water becomes really progressive, for then, as it cannot sink directly downwards, it falls over and forwards, seeking the level. So awful is the spectacle of a storm at sea, that it generally biases the judgment; and, lofty as waves really are, imagination pictures them loftier still. Now no wave rises much more than ten feet above the ordinary sea- level, which, with the ten feet that the surface afterwards descends below this, give twenty feet for the whole height, from the bottom of any water- valley to an adjoining summit. This is easily verified by a person who tries at what heighten a ship's mast the horizon remains always in sight over the top of the waves allowance being made for accidental inclinations of the ves- sel, and for her sinking in the water to considerably below her water line, at the time when she reaches the bottom of the hollow between the two waves. The spray of the sea, driven along by the violence of the wind, is of course much higher than the summit of the liquid wave ; and a wave coming against an obstacle, or entering a narrow inlet, may dash to an elevation much greater still. At Eddystone light house, which is about ninety feet high, placed on a solitary rock ten miles from land, when a surge breaks which has been growing under a storm all the way across the Atlantic, it often dashes to 100 feet above the lantern at the summit. The magnitude of waves is well judged of when they are seen breaking WAVES. 219 on an extended shore or beach. In the deep sea the wave is only an eleva- tion of the water, sloping on either side ; but as it rolls towards the shore, its front becomes more and more perpendicular, until at last it curls over and falls with its whole weight, and when several miles of it break at the same instant, its force and noise may shake- the country abroad. Along the east, or Corom-andel Coast of India, at certain season, vast waves are constantly breaking ; and as there are no good harbours there, com- munication between the sea and land is rendered impossible to ordinary boats. The natives of the coast, at Madras, for instance, have hence become almost amphibious. They reach ships beyond the breakers by the help of what are called catamarans, consisting of three small logs of wood tied together. On these they secure themselves, and boldly advance up to the coming wall of water, which they shoot into, and rise to the smooth surface beyond it, like water-fowls after diving. Boats unsuited to the breakers often perish in them. The author of this work had gone on shore with a watering party on the coast of Sumatra, and during the hours spent there, a swell had risen in the sea, which on their return was already bursting along the beach and across the river's mouth in lofty breakers. The boat in which he happened to be, regained the high sea in safety, but a larger boat which followed at a short distance was overwhelmed, and an officer and part of the crew perished. There is a phenomenon observed at the mouths 01* many great rivers, called the Boar, which has resemblance to a wave. When the tide returning from sea meets the outward current from the river, and both have the force which in certain situations belongs to them, the stronger mass from the ocean assumes the form of an almost perpendicular wall, moving inland with resistless sweep. This is called the boar. It is in fact the great sea-wave of the tide, produced twice a-day by the attraction of the moon, rolling in upon the land and inlets, where contracting channels concentrate its mass. In the different branches of the Ganges the boar is seen in a remarkable degree. Its roaring is heard long before it arrives. Smaller boats and skiffs cannot live where it comes ; and as it passes the city of Calcutta, even the large ships at anchor there are thrown into such commotion, as sometimes to be torn away from their moorings. The nature and effects of this boar are strikingly illustrated upon certain coasts where extensive tracts of sand are left uncovered at low water. In such situations, of which there are many on the western shores of Britain, the returning tide is seen advancing with steep front, and with such rapidity, that the speed of a galloping horse can scarcely save a person who has incautiously approached too near. Many, every year, are the victims of temerity or ignorance on these treacherous plains. In the end of the year 1831, on the low flat coast of the Indian peninsula, north of Madras, one great wave of the kind now described was produced during a very high-spring tide of midnight, by an extraordinary wind, and spread ten miles in upon the inhabited land. It had retired with the ebbing tide before morning, but the next day's sun disclosed a scene of devastation rarely matched. Amidst the total wreck of the villages and fields, there lay the drowned carcases of more than ten thousand human beings, mixed with those of elephants, horses, bullocks, wild tigers and the other inhabitants of the land. It has been proposed lately to construct sub-marine boats, or vessels cal- culated to swim so deep in the water as to be below the superficial motion of the waves, and therefore beyond the influence of storms at the surface. Such a boat has been tried with considerable success; and man's increasing fami- liarity with sub-marine matters since the invention of the diving-bell, may 220 HYDRAULICS. ultimately lead to improvements rendering the sub-marine vessel, for certain purposes, commodious and safe. " Fluids resisting the motion of bodies immersed in them, or themselves moving forcibly against other bodies.'' (See the Analysis.) The same force is required to give or to take away, or to bend motion, in a fluid, as in an equal quantity of solid matter. A pound of water enclosed in a bladder is not more easily thrown to a given height than a pound of ice or of lead; nor, if falling into the scale of a weighing beam, does it require less as a counterpoise ; nor, if made to revolve at the end of a sling, does it render the cord less tight. A convenient measure of the force of moving water on an obstacle, or of the resistance of still water to a moving body, exists in the facts already explained, that the pressure of a known height of fluid column produces from an orifice a certain velocity of jet, while conversely, that jet, or a current of equal speed, directed against the orifice supports the column. The impulse given or received, therefore, by a flat surface in water, such as the vane of a water-wheel, whether that of a steam-boat pressing against the water, or that of a corn-mill pressed by it, is measured by the weight of the column alluded to, the height of which is, according to the velocity and the breadth or diameter, according to the breadth or extent of the solid surface concerned. This estimate supposes that the pressure of air upon the surface is direct ; if it be oblique, there is a diminution according to the rule given under the head of " resolution of forces." Many persons looking carelessly at the subject of fluid resistance, would expect that if a body, as a boat, moving through a fluid at a given rate, meets a given resistance, it should just meet double resistance when moving twice as fast. Now the resistance is four times greater with a double rate. This fact is but another example of a principle already explained, and when more closely examined, is easily understood. A boat which moves one mile per hour, displaces or throws aside a certain quantity of water, and with a certain velocity ; if it move twice as fast, it of course displaces twice as many particles at the same time, and requires to be moved by twice the force on that account; but it also displaces every particle with a double velocity, and requires another doubling of the power on this account; the power then being doubled on two accounts becomes a power of four. In the same manner with a speed of three, three times as many particles are moved and each particle with three times the velocity; therefore, to overcome the resistence, a force of nine is wanted ; for a speed of four, a power of sixteen ; for a speed of five, a power of twenty-five, and so forth : the relations being that which mathematicians indicate by saying that the resistance increases as the square of the speed. The corresponding numbers, up to a speed of ten are as here shown. Speed ..123456789 10 Correspondingj j 9 16 25 36 49 64 81 100 resistance j Thus, if even the resistance at the bow of a vessel was all that had to be considered, the force of one hundred horses would only drag the vessel ten times as fast as the force of one horse. But there is another important element in the calculation, viz ; the lessening, as the vessel's speed quick- WAVES. 221 ens, of the usual water pressure on the stern, which pressure while she is at rest is equal to the pressure on the bow, and the force therefore required to produce an increased velocity is still considerably greater than as noted in the table. There is not a more important truth in, physics than the law of fluid assistance to moving bodies here treated of; .it explains so many phenomena of nature, and becomes a guide in so many matters of art. We will now set forth some interesting examples. It explains at what a heavy expense of coal high velocities are obtained in steam-boats. If an engine of about 50 horse power would drive a boat 7 miles an hour, two engines of 50, or one of 100 would be required to drive it 10 miles, and three such to drive it 12 miles, even supposing the increased resistance to the bow, as already stated, to be the measure of the whole work done, which it is not, and that engines worked to the same advantage with a high velocity as with a low, which they do not. For the same reasons, if all the coal which a ship could conveniently carry were just sufficient to drive her 1,000 miles, at a rate of 12 miles per hour, it would drive her more than 3,000 at a rate of 7 miles per hour; and more than6,000 at a rate of 5 miles per hour. This is a very important consideration for persons concerned in steam navigation to distant parts. The same law shows the folly of putting very large sails on a ship; the trifling advantage in point of speed by no means compensating for the addi- tional expense of making and working the sails, and the risk of accidents in bad weather. The ships of the prudent Chinese have not, for the same tonnage, one-third so much sail as those of Europeans, and yet they move but little slower on that account. A European ship under jury-masts does not lose so much of her usual speed as most people would expect. This law explains also why a ship glides through the water one or two miles an hour when there is very little wind, although with a strong breeze she would only sail at the rate of eight or ten miles. Less than the 100th part of that force of wind which drives her ten miles an hour, will drive her one mile per hour, and less than the 400th part will drive her half a mile. Thus, also, during a calm, a few men pulling in a boat can move a large ship at a sensible rate. These considerations show strikingly of what importance to navigation it might be to have, as a part of a ship's ordinary equipment, one or two water- wheels, ( or ready means of forming them,) to be affixed upon the ship's side when required, like the paddle-wheels of a steam-boat, and by turning which, the crew might easily deliver themselves from the tedium, or even disastrous consequences of a long calm at sea. This idea occurred to the author while in a ship completely becalmed for weeks on the Line : during which weari- some periods, the breezes were often seen roughening the water a mile or two farther on ; and any means that could have enabled the ship's company to advance her that little distance might have saved the delay. The wheels might be driven by connection with the capstan, at which, under such circumstances, the crew would most willingly work. Delay in a large vessel often costs hundreds of pounds per day, and may retard the execution of important projects. But the propelling of a ship in a calm seems, by no means, the most important purpose which such wheels might serve. If from disease, fatigue, or other cause, the crew were inadequate to existing necessities, two wheels affixed to the extremities of an axis crossing the ship might be equivalent in many cases to additional hands, or to a steam-engine of great power ; for when acted upon by the water as the ship sailed, they 222 HYDRAULICS. would turn with the force of water-wheels on shore, and might be made to move the pumps ; to hoist the sails, and to do any work which a steam-engine could perform. Many a gallant vessel has perished because the exhausted crew could not longer labour at the pumps, where such water-wheels as now contemplated, or a wind-mill wheel in the rigging would have performed the duty most perfectly. The law that resistance to a body moving in a fluid increases in a greater proportion than in speed of Ihe body, applies where the fluid is aeriform, as well as where it is liquid. A bullet shot through the air with a double velocity, for the reason assigned above, experiences four times as much resistance in front, as with a single velocity : the motion is retarded also by the diminution of the usual atmospheric pressure of 15 Ibs. per inch on the posterior surface, which diminution is proportioned to the speed. It is farther true, that when the velocities of bodies moving in the air are very great, the resistance increases in a still quicker ratio than in liquids, probably because the compressibility of air allows it to be much condensed or heaped up before the quick moving body. It is useless to discharge a cannon-ball with a velocity exceeding 1,200 feet in a second, because the powerful resistance of the air to any velocity beyond that, soon reduces it to that at least. The rule of reciprocal action between a solid and fluid, now explained, holds equally when the fluid is in motion against the solid, as when the solid moves through the fluid. If a ship be anchored in a tide's way, where the current is four miles an hour, the strain on her cable is not one fourth part so great as if the current were eight miles. A wind moving three miles an hour is scarcely felt : if moving six miles, it is a pleasant breeze ; if twenty or thirty miles, it is a brisk gale ; if sixty, it is a storm; and beyond eighty, it is a frightful hurricane, tearing up trees and destroying every thing. Supposing the wind to move one hundred miles per hour, there are one hundred times as many particles of matter striking any body exposed to it, as when it moves only one mile per hour, and each particle strikes, more- over, with one hundred times the velocity or force, so that the whole increase of force is a hundred times a hundred, or ten thousand. This explains how the soft invisible air may by motion acquire force sufficient to unroof houses, to level oaks which have been stretching their roots around for a century, and in some West India hurricanes, absolutely to brush every projecting thing from the surface of the earth. The law of rapidly increasing resistance assigns a limit to many velocities, both natural and artificial. It limits the velocity of bodies falling through the air. By the law of gravity, a body would fall with a constantly accelerating speed, but as the resistance of the air increases still more quickly than the speed at a certain point, this resistance and the gravity balance each other, and the motion becomes uniform* ACTION BETWEEN FLUIDS AND SOLIDS. 223 The parachute, by means of which a person may safely descend to the* earth from a balloon at any elevation, furnishes a good example. The con- trivance resembles a large flat umbrella. The aeronaut attaches himself underneath it, and when it is let loose from the balloon, he is partly sup- ported by the resistance which its broad expanse experiences in falling through the air, tind falls, therefore, in a corresponding degree more slowly. After the first second or two, for the reason stated above, it descends with a uniform motion ; and its breadth is generally made such, as to allow a velocity of about eleven feet in a second, or that which a man acquires in jumping from a chair two feet high. No ship sails faster than fifteen miles in an hour. And it is because the resistance to be overcome in steam-carriages on rail-ways, viz., their friction, does not increase with their velocity like the fluid resistance to steamboats, that the speed of the former may so much exceed that of the latter. No fish swims with a velocity exceeding twenty miles an hour; not the dolphin, when shooting ahead of our swiftest frigates, nor the salmon, when darting forward with a speed which lifts him over the water-fall. And the flight of birds through the thin air has a limited celerity. The crow, when flying homewards against the storm, cannot face the wind in the open sky, but skims along the surface of the earth in the deep valleys, or wherever the swiftness of the wind is retarded by terrestrial obstructions. The great albatross, stemming upon the wing the current of a gale so as to keep company with a driving ship where the air is passing at the rate of a hundred miles an hour, often takes shelter momentarily under the lee-side of the lofty billows. The bird called the stormy petrel abides chiefly in the midst of the Atlantic Ocean, but the irresistible violence of the wind occa- sionally sweeps it from the waves, and causes its appearance on the western shores of Europe. Vessels from the high sea, approaching a coast from which the wind blows, generally become resting places to exhausted land birds driven off the shore by wind which they have not had strength of wing to stem ; sad evidences of the myriads which are constantly perishing where no resting place is found, and where no human eye notes their fate. The action or resistance between a meeting fluid and solid, is influenced by the shape of the solid. This follows from what has already been said of direct and oblique impulse. If a flat surface directly opposed to the fluid experience a certain resistance, a projecting surface like that of a sphere or short wedge is resisted in a less degree, and a concave surface in a greater. The explanation is, that a flat or plane surface throws the particles of fluid almost directly outwards from its centre to its circumference, and therefore with greater velocity, while the convex or wedge-like surface, although displacing them just as far, still does so more slowly, and therefore with less expenditure of force, in proportion to the obliquity of surface, or as its point is in advance of its shoulder or broadest part ; and a concave surface must give to some of the particles a forward as well as lateral motion. The shape of the hinder part of a solid moving through a fluid is of importance for corresponding reasons. The following are instances of projecting or wedge-like surfaces, intended to diminish the resistance. Fishes are wedge-like, both before and behind, their form being modified, however, in relation to other objects than mere speed of motion. Birds are so, also ; and they stretch out their necks while flying, so as to make their form perfect for dividing the air. In the form 224 HYDRAULICS. f)f the under part of boats and ships, men have, in a degree, imitated the shape of fishes. The light wherries which shoot about upon the surface of the Thames, appear the very essence of what imagination can picture of form combining utility and grace. There are boats used in China called snake- boats, which are only a foot or two broad, but perhaps a hundred feet in length, and when moved, as they often are, by nearly a 'hundred rowers, their swiftness is extreme. The problem of which it is the object to assign for a ship's hull or. bottom the best possible form that she may have speed of sailing, is not yet completely solved; so that a kind of empiricism prevails in the matter, and very unexpected results often arise. Yet the subject merits much attention, for when vessels have to chase and to flee, speed becomes of the greatest importance; and at all times the sailor's heart swells with delight to find his well-beloved vessel performing well. The following instances exhibit the mutual influence of meeting solids and fluids, where the surface of the solid is plane or concave. In a water-wheel, whether the water be moving against the wheel, as is the case where a stream acts to drive machinery, or the. wheel be moving against the still water, as in the case of the paddle-wheels of a steam-boat, the extended faces of the vanes or float-boards give or receive a powerful impulse. When a wheel with float-boards has its lower part merely dipping into a stream of Water, to be driven by the momentum, it is called an undershot-wheel; when the water reaches the wheel near the middle of its height, and turns it by falling on the float-boards of one side as they sweep downwards in a curved trough fitting them, the modification is called a breast-wheel ; and when the float- boards are shut in by flat sides, so as to become the bottoms of a circle of cavities or buckets surrounding the wheel, into which the water is allowed to fall at the top of the wheel, and to act by its weight instead of its momen- tum, the modification is called the overshot-wheel. To have a maximum of effect from wheels moved by the momentum of water, they are generally made to turn with a velocity about one-third as great as that of the water ; and wheels moved by the simple weight of water usually have their circum- ference turning with a velocity of about three feet per second. The subject of water-wheels is one of the most important in practical mechanics ; for moving water performs a great deal of labor for man. Oars for boats are made flat, and often a little concave, that the mutual action between them and water may be as great as possible. The webbed feet of water-fowl are oars ; in advancing, they collapse like a shutting um- brella, but open outwards in the thrust backwards, so as to offer a broad concave surface to the water. The expanded wings of birds are in like manner a little concave towards the air which they strike. The sails of ships, when they are receiving a fair wind, are left slack so as to swell and become hollow. The resistance between a meeting solid and fluid being nearly proportioned to the breadth of the solid, it follows that large bodies, because containing more matter in proportion to their breadth or surface than smaller bodies of similar form, are less resisted in proportion to their weights, than smaller bodies. The science of measures tells us that a bullet or other solid of two inches diameter, has eight times as much matter in it as a similar solid of one inch diameter, while it has only four time the breadth or surface. Thus, by putting eight dice or little cubes together, as here represented, we have a ACTION BETWEEN FLUIDS AND SOLIDS. 225 larger cube, of which compared with a single dice, the edge is evidently twice as long, the surface four times as great ; and the quantity of matter eight times as great; again, twenty -seven dice simi- larly put together form a cube with sides three times Fig. 109. as long, and the surface nine times as great ; and sixty- four dice form a cube with sides four times as long, and a surface sixteen times as great. All solids similar M^TL- have to each other this kind of relation, which, in the language of the science of quantity, is called the rela- tion of cubes : they are said to be to each other as the cubes of any of their corresponding lines. Hence if a bullet of eight pounds, and a bullet of one pound be shot off with equal velocity, because that of eight pounds has only half as much surface in pro- portion to its weight, and therefore to its moral inertia or force, as the other, it will go much farther than the other. This important rule explains why shells and large shot may be thrown four or five miles, while smaller cannon-balls, musket-bullets, pistol and swan shot, and the common small shot of the sportsman, all of which are generally discharged from their respective pieces with the same commencing velocity, have a shorter range, as the size of the projectile is less. Even water is sometimes thrown from a gun or powerful syringe to stun birds, that they may be obtained with uninjured plumage ; but it soon divides in the air so minutely that it reaches only a short distance. Water falling through the air from a great height, goes on suffering a gradual division into smaller and smaller portions, which at last may be said to be nearly all surface : and then the resistance of the air lets them fall very slowly indeed. The relation of the size and resistance is well shown by the difference of celerity in the descent of a minute fog, a drizzling mist, and common rain. The toy called the iuater-hammcr, is merely a little water enclosed in a tube exhausted or empty of air ; and when, by turning the tube, the water is made to fall from one end to the other, as there is no air to impede or divide it in its descent, it falls as one mass, and makes a sharp noise like the blow of a hammer. The same law explains why a spider's thread or a single filament of silk floats so long in the air before it falls; why there is almost constantly sus- pended in the air, wherever active man resides, that immense quantity of very minute solid particles, which when rendered visible by the sun's light passing directly through them, are called motes in the sunbeam particles of which are constantly settling on household furniture, and rendering necessary the daily operation of dusting or cleaning; why the fine dust sent aloft during the eruption of volcanoes is often carried by the wind to a distance of hundreds of miles; why in the deserts of Africa the strong winds often transport fine sand from place to place, overwhelming caravans, and forming new mountains, which succeeding blasts are again to lift; why in the bottom of a river, or in a tides-way, fine mud is found where the current is slow ; sand where it is quicker ; pebbles, or large stones, where it is quicker still j while in rapids and water-falls, only massy rocks can resist the fluid force. Now .rocks, pebble, sand and mud, may all be the same material in portions of different magnitude. This law explains the operation of levigating, by which substances inso- luble in water are obtained in the state of a very fine powder. Any such substance is first ground or powdered in the ordinary way, and mixed with water. The grosser parts then soon fall to the bottom, while the fine dust 15 226 HYDRAULICS. t. remains longer suspended. This is afterwards obtained separately by pour- ing the fluid which bears it into another vessel, and allowing more time for the slow subsidence. The fine powder of flint used in the manufacture of porcelain is obtained by levigation as is also that of calamine stone ; and other powders used in medicine and various arts. This law farther explains how, by means of air or water, bodies of differ- ent specific gravities, although mixed ever so intimately, may be easily separated. If pieces of cork, and lead be let fall together through the air, the lead will reach the ground first, and may be swept away before the cork arrives ; but in a vacuum the whole would reach the ground at the same time as is proved by the common experiment of the guinea and feather falling in the exhausted receiver of an air-pump. Again, when a mixture of corn and chaff, as it comes from any threshing machine, is showered down from a sieve in a current of air, the chaff being longer in falling, is carried farther by the wind, while the heavier corn falls almost perpendicularly. The farmer, therefore, by winnoioing in either a natural or artificial current of air, readily separates the grain from the chaff; and, if he desire it, may even divide the grain itself into portions of different quality. Similar to the operation of separating chaff from corn by wind, is that of separating sand or mud from gold-dust by water : the soil containing gold-dust is first spread on a flat surface, over which a current of water is then made to pass \ which current carries away the lighter rubbish, and leaves the gold. If a mass of metal be affixed on the end of a rod of wood, the rod then, whether simply falling through the air, or advancing as an arrow, will follow the heavier metal as its points. The cork of a shuttlecock is always foremost for the same reason. The instances enumerated under this head serve to show how many and varied the results may be which flow from a single principle. When a fluid and a solid meet each other obliquely, the impulse or effect is still perpendicular to the surface of the solid, as if they met directly, but is less forcible as the obliquity of the approach is greater. Suppose a b to represent the upper edge of a smooth board or of any flat polished surface, standing in a current, the fluid approaching this surface in whatever direction, must act upon it as if approaching perpendicularly, because on account of its smoothness, the fluid can take Fig. 110. no hold of it to push it endways, either towards a or b. But the impulse of a stream acting on the surface will be less forcible if the surface be oblique to the stream, both because less fluid will touch, and because the velo- city of the effective approach will be less. The line c d marks the breadth, and therefore force, of the part of a stream reaching the board directly ; and the shorter line/c marks the smaller breadth that can touch it, of a stream coming obliquely in the direction c I : in the oblique stream, moreover, if the line c b mark the whole velocity, the shorter line c a marks the slower rate of the direct approach of any one particle to the board. (This subject was treated of at page 57, under the head of Resolution of Forces.) Hence the wind blowing upon the sail of a ship, however obliquely OBLIQUE FLUID ACTION. 227 Fig. 112. CL always presses it directly forward or perpendicularly Fig. 111. to its surface, but acts less forcibly as the obliquity is greater. If the wind be represented, as to direction and strength, by the line ed approaching the sail a b, it will act on the sail as if it came from/*, but with the smaller force f d, instead of the whole force e d. The effect, therefore, is the same as if the sail were pulled by the rope d c. We see in this how a ship can be made to sail in a certain degree against the wind > for all the sails being.adjusted so as to receive the wind in the direction here shown, they all act to produce the same result as if ropes were pulling from each in the direction of dc; and a force like/c?, or a rope like